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700 | On the Removable Singularities for Meromorphic Mappings | math.CV | If E is a nonempty closed subset of the locally finite Hausdorff
(2n-2)-measure on an n-dimensional complex manifold M and all points of E are
nonremovable for a meromorphic mapping of M \ E into a compact K\"ahler
manifold, then E is a pure (n-1)-dimensional complex analytic subset of M. | math |
701 | Szegö kernels for certain unbounded domains in $\Bbb C^2$ | math.CV | No abstract available. | math |
702 | Domains in $\cx {n+1}$ with Noncompact Automorphism Group. II | math.CV | No abstract available. | math |
703 | Zero sets of some classes of entire functions | math.CV | A method of constructing an entire function with given zeros and estimates of
growth is suggested. It gives a possibility to describe zero sets of certain
classes of entire functions of one and several variables in terms of growth of
volume of these sets in certain polycylinders. | math |
704 | Analytic varieties versus integral varieties of Lie algebras of vector fields | math.CV | We associate to any germ of an analytic variety a Lie algebra of tangent
vector fields, the {\it tangent algebra}. Conversely, to any Lie algebra of
vector fields an analytic germ can be associated, the {\it integral variety}.
The paper investigates properties of this correspondence: The set of all
tangent algebras is ... | math |
705 | Holomorphic curvature of Finsler metrics and complex geodesics | math.CV | In his famous 1981 paper, Lempert proved that given a point in a strongly
convex domain the complex geodesics (i.e., the extremal disks) for the
Kobayashi metric passing through that point provide a very useful fibration of
the domain. In this paper we address the question whether, given a smooth
complex Finsler metric... | math |
706 | Sequences of analytic disks | math.CV | The subject considered in this paper has, at least, three points of interest.
Suppose that we have a sequence of one-dimensional analytic varieties in a
domain in $\Bbb C^n$. The cluster of this sequence consists from all points in
the domains such that every neighbourhood of such points intersects with
infinitely many... | math |
707 | A counterexample to the Arakelyan Conjecture | math.CV | A ``self--similar'' example is constructed that shows that a conjecture of N.
U. Arakelyan on the order of decrease of deficiencies of an entire function of
finite order is not true. | math |
708 | The Green function of Teichmüller spaces with applications | math.CV | We describe briefly a new approach to some problems related to Teichm\"uller
spaces, invariant metrics, and extremal quasiconformal maps. This approach is
based on the properties of plurisubharmonic functions, especially of the
plurisubharmonic Green function. The main theorem gives an explicit
representation of the Gr... | math |
709 | Radó theorem and its generalization for CR-mappings | math.CV | The following theorem is proved:
Let M be a locally Lipschitz hypersurface in C^n with one-sided extension
property at each point (e.g., without analytic discs). Let S be a closed subset
of M and f : M \ S ---> C^m \ E is a CR-mapping of class L^{\infty} such that
the cluster set of f on S along of Lebesque points of... | math |
710 | Complexity of the classical kernel functions of potential theory | math.CV | We show that the Bergman, Szego, and Poisson kernels associated to a finitely
connected domain in the plane are all composed of finitely many easily computed
functions of one variable. The new formulas give rise to new methods for
computing the Bergman and Szeg\H o kernels in which all integrals used in the
computation... | math |
711 | Moduli of bounded holomorphic functions in the ball | math.CV | We prove that there is a continuous non-negative function $g$ on the unit
sphere in $\cd$, $d \geq 2$, whose logarithm is integrable with respect to
Lebesgue measure, and which vanishes at only one point, but such that no
non-zero bounded analytic function $m$ in the unit ball, with boundary values
$m^\star$, has $|m^\... | math |
712 | Complex Finsler metrics | math.CV | In this paper we describe an approach to complex Finsler metrics suitable to
deal with global questions, and stressing the similarities between hermitian
and complex Finsler metrics. Let $F$ be a smooth complex Finsler metric on a
complex manifold $M$, and assume that the indicatrices of $F$ are strongly
pseudoconvex -... | math |
713 | Quasiconformal Homeomorphisms on CR 3-Manifolds With Symmetries | math.CV | An extremal quasiconformal homeomorphisms in a class of homeomorphisms
between two CR 3-manifolds is an one which has the least conformal distortion
among this class. This paper studies extremal quasiconformal homeomorphisms
between CR 3-manifolds which admit transversal CR circle actions. Equivariant
$K$-quasiconforma... | math |
714 | Regularity And Extremality Of Quasiconformal Homeomorphisms On CR 3-Manifolds | math.CV | This paper first studies the regularity of conformal homeomorphisms on smooth
locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve
families are used to estimate the maximal dilatations of quasiconformal
homeomorphisms. On certain CR 3-manifolds, namely, CR circle bundles over flat
tori, extremal ... | math |
715 | Pseudo-periodic homeomorphisms and degeneration of Riemann surfaces | math.CV | We will announce two theorems. The first theorem will classify all
topological types of degenerate fibers appearing in one-parameter families of
Riemann surfaces, in terms of ``pseudoperiodic'' surface homeomorphisms. The
second theorem will give a complete set of conjugacy invariants for the mapping
classes of such ho... | math |
716 | Cartwright-type and Bernstein-type theorems for functions analytic in a cone | math.CV | Cartwright-type and Bernstein-type theorems, previously known only for
functions of exponential type in $\C^n$, are extended to the case of functions
of arbitrary order in a cone. | math |
717 | Entire periodic functions with plane zeros | math.CV | We give a complete description of divisors of entire periodic functions in
$\C^n$ with plane zeros. | math |
718 | CR manifolds with noncompact connected automorphism groups | math.CV | The main result of this paper is that the identity component of the
automorphism group of a compact, connected, strictly pseudoconvex CR manifold
is compact unless the manifold is CR equivalent to the standard sphere. In
dimensions greater than 3, it has been pointed out by D. Burns that this result
follows from known ... | math |
719 | Continuity of the complex Monge-Ampere operator | math.CV | The complex Monge-Amp\`ere operator $(dd^c)^n$ is an important tool in
complex analysis. It would be interesting to find the right notion of
convergence $u_j\to u$ such that $(dd^cu_j)^n\to (dd^cu)^n$ in the weak
topology. In this paper, using the $C_{n-1}$-capacity, we give a sufficient
condition of the weak convergen... | math |
720 | The Kobayashi metric for non-convex complex ellipsoids | math.CV | In the paper we give some necessary conditions for a mapping to be a
$\kappa$-geodesic in non-convex complex ellipsoids. Using these results we
calculate explicitly the Kobayashi metric in the ellipsoids
$\{|z_1|^2+|z_2|^{2m}<1\}\subset\bold C^2$, where $m<\frac12$. | math |
721 | Propagation of Gevrey Regularity for a Class of Hypoelliptic Equations | math.CV | We prove results on the propagation of Gevrey and analytic wave front sets
for a class of $C^\infty$ hypoelliptic equations with double characteristics. | math |
722 | Global (and Local) Analyticity for Second Order Operators Constructed from Rigid Vector Fields on Products of Tori | math.CV | We prove global analytic hypoellipticity on a product of tori for partial
differential operators which are constructed as rigid (variable coefficient)
quadratic polynomials in real vector fields satisfying the H\"ormander
condition and where $P$ satisfies a `maximal' estimate. We also prove an
analyticity result that i... | math |
723 | The Lu Qi-Keng Conjecture Fails Generically | math.CV | The bounded domains of holomorphy in~$\mathbf{C}^n$ whose Bergman kernel
functions are zero-free form a nowhere dense subset (with respect to a variant
of the Hausdorff distance) of all bounded domains of holomorphy. | math |
724 | On the reflection principle in C^n | math.CV | We propose a reflection principle for holomorphic objects in ${\Bbb C}^n$.
Our construction generalizes the classical principle of H.Lewy, S.Pinchuk and
S.Webster. | math |
725 | Unbounded Symmetric Homogeneous Domains in Spaces of Operators | math.CV | We define the domain of a linear fractional transformation in a space of
operators and show that both the affine automorphisms and the compositions of
symmetries act transitively on these domains. Further, we show that Liouville's
theorem holds for domains of linear fractional transformations, and, with an
additional t... | math |
726 | On extremal mappings in complex ellipsoids | math.CV | In the paper we generalize the notion of problem (P) introduced by Poletsky.
We introduce the notion of (P_m) extremals. For example, geodesics are (P_1)
extremals. Using obtained results we present a description of (P_m) extremals
in arbitrary complex ellipsoids. It is a generalization of the result obtained
by Jarnic... | math |
727 | Shulim Kaliman and Mikhail Zaidenberg | math.CV | No abstract available. | math |
728 | Regularity of CR mappings between algebraic hypersurfaces | math.CV | We prove that if $M$ and $M'$ are algebraic hypersurfaces in $ C^ N$, i.e.
both defined by the vanishing of real polynomials, then any sufficiently smooth
CR mapping with Jacobian not identically zero extends holomorphically provided
the hypersurfaces are holomorphically nondegenerate . Conversely, we prove that
holomo... | math |
729 | Fixed points of elliptic reversible transformations with integrals | math.CV | We show that for a certain family of integrable reversible transformations,
the curves of periodic points of a general transformation cross the level
curves of its integrals. This leads to the divergence of the normal form for a
general reversible transformation with integrals. We also study the integrable
holomorphic ... | math |
730 | Divergence of the normalization for real Lagrangian surfaces near complex tangents | math.CV | We study real Lagrangian analytic surfaces in C^2 with a non-degenerate
complex tangent. Webster proved that all such surfaces can be transformed into
a quadratic surface by formal symplectic transformations of C^2. We show that
there is a certain dense set of real Lagrangian surfaces which cannot be
transformed into t... | math |
731 | Integrable analytic vector fields with a nilpotent linear part | math.CV | We study the normalization of integrable analytic vector fields with a
nilpotent linear part. We prove that such an analytic vector field can be
transformed into a certain form by convergent transformations when it has a
non-singular formal integral. In particular, we show that a formally
linearizable analytic vector f... | math |
732 | Unimodular invariants of totally real tori in C^n | math.CV | We study the global invariants of real analytic manifolds in the complex
space with respect to the group of holomorphic unimodular transformations. We
consider only totally real manifolds which admits a certain fibration over the
circle. We find a complete set of invariants for totally real tori in C^n which
are close ... | math |
733 | Circle Packings in the Unit Disc | math.CV | A Bl-packing is a (branched) circle packing that ``properly covers'' the unit
disc. We establish some fundamental properties of such packings. We give
necessary and sufficient conditions for their existence, prove their
uniqueness, and show that their underlying surfaces, known as carriers, are
quasiconformally equival... | math |
734 | A characterization of the finite multiplicity of a CR mapping | math.CV | No abstract available. | math |
735 | The Several Complex Variables Problem List | math.CV | The purpose of this bulletin board is to collect problems in higher
dimensional complex analysis. We are interested both in basic research
questions as well as interactive questions with other fields and sciences. We
encourage everybody to submit problems to the list. This includes not only
those coming up in your own ... | math |
736 | On $\bold N$-circled $\bold{H^\infty}$-domains of holomorphy | math.CV | We present various characterizations of $n$-circled domains of holomorphy
$G\subset\CC^n$ with respect to some subspaces of $\Cal H^\infty(G)$. | math |
737 | Algebraicity of holomorphic mappings between real algebraic sets in ${\bold C}^n$ | math.CV | We give conditions under which a germ of a holomorphic mapping in $\Bbb C^N$,
mapping an irreducible real algebraic set into another of the same dimension,
is actually algebraic.
Let $A\subset \bC^N$ be an irreducible real algebraic set. Assume that there
exists $\po \in A$ such that $A$ is a minimal, generic, holomo... | math |
738 | Reinhardt Domains with Non-Compact Automorphism Groups | math.CV | We give an explicit description of smoothly bounded Reinhardt domains with
noncompact automorphism groups. In particular, this description confirms a
special case of a conjecture of Greene/Krantz. | math |
739 | Finite Type Conditions on Reinhardt Domains | math.CV | In this paper we prove that, if $p$ is a boundary point of a smoothly bounded
pseudoconvex Reinhardt domain in $\C^n$, then the variety type at $p$ is
identical to the regular type. | math |
740 | A stabilization theorem for Hermitian forms and applications to holomorphic mappings | math.CV | We consider positivity conditions both for real-valued functions of several
complex variables and for Hermitian forms. We prove a stabilization theorem
relating these two notions, and give some applications to proper mappings
between balls in different dimensions. The technique of proof relies on the
simple expression ... | math |
741 | Interpolating sequences for weighted Bergman spaces of the ball | math.CV | Let $B_{\alpha}^{p}$ be the space of $f$ holomorphic in the unit ball of
$\Bbb C^n$ such that $(1-|z|^2)^\alpha f(z) \in L^p$, where $0<p\leq\infty$,
$\alpha\geq -1/p$ (weighted Bergman space). In this paper we study the
interpolating sequences for various $B_{\alpha}^{p}$. The limiting cases
$\alpha=-1/p$ and $p=\inft... | math |
742 | Global $C^\nf$ Irregularity of the $\bar\partial$--Neumann Problem for Worm Domains | math.CV | No abstract available. | math |
743 | On Analytic Solvability and Hypoellipticity For $\dbar$ and $\dbar_b | math.CV | No abstract available. | math |
744 | Nonexistence of Continuous Peaking Functions | math.CV | We construct a smoothly bounded pseudoconvex domain such that every boundary
point has a p.s.h. peak function but some boundary point admits no (local)
holomorphic peak function. | math |
745 | The monodromy groups of Schwarzian equations on closed Riemann surfaces | math.CV | Let \theta:\pi_1(R) \to \PSL(2,\C) be a homomorphism of the fundamental group
of an oriented, closed surface R of genus exceeding one. We will establish the
following theorem.
Theorem. Necessary and sufficient for \theta to be the monodromy
representation associated with a complex projective stucture on R, either
unb... | math |
746 | Regularity of Holomorphic Correspondences and Applications to the Mapping Problems | math.CV | We study the regularity results of holomorphic correspondences. As an
application, we combine it with certain recently developed methods to obtain
the extension theorem for proper holomorphic mappings between domains with real
analytic boundaries in the complex 2-space. | math |
747 | An Example of a Domain with Non-Compact Automorphism Group | math.CV | We give an example of a bounded, pseudoconvex, circular domain in ${\mathbb
C}^3$ with smooth, real-analytic boundary and non-compact automorphism group,
which is not biholomorphically equivalent to any Reinhardt domain. | math |
748 | Examples of domains with non-compact automorphism groups | math.CV | We give, in dimensions three or greater, an example of a bounded,
pseudoconvex, circular domain in complex space with smooth real analytic
boundary and non-compact automorphism group which is not biholomorphically
equivalent to any Reinhardt domain. We give an analogous example in dimension
two, but the domain fails to... | math |
749 | On the product property of the pluricomplex Green function | math.CV | We prove that the pluricomplex Green function has the product property
$g_{D_1\times D_2}=\max\{ g_{D_1},g_{D_2}\}$ for any domains $D_1\subset\Bbb
C^n$ and $D_2\subset\Bbb C^m$. | math |
750 | Divergence of projective structures and lengths of measured laminations | math.CV | Given a complex structure, we investigate diverging sequences of projective
structures on the fixed complex structure in terms of Thurston's
parametrization. In particular, we will give a geometric proof to the theorem
by Kapovich stating that as the projective structures on a fixed complex
structure diverge so do thei... | math |
751 | CR automorphisms of real analytic manifolds In complex space | math.CV | In this paper we shall give sufficient conditions for local CR
diffeomorphisms between two real analytic submanifolds of $\Bbb C^N$ to be
determined by finitely many derivatives at finitely many points. These
conditions will also be shown to be necessary in model cases. We shall also
show that under the same conditions... | math |
752 | Errata for Geometric Function Theory in Several Complex Variables | math.CV | This is a list of corrections for the book: J. Noguchi and T. Ochiai,
Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\
Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors
hope that this distribution will be helpful for readers to avoid unnecessary
confusions. | math |
753 | Nonvanishing of the differential of holomorphic mappings at boundary points | math.CV | In this paper we prove a general result of the ``Hopf lemma'' type for CR
mappings, with nonidentically vanishing Jacobians, between real hypersurfaces
in C^n with smooth or real analytic boundaries. Applications of this result to
finiteness and holomorphic extendibility of such mappings are also given. The
novelty her... | math |
754 | An interpolation theorem for holomorphic automorphisms of {\bf C}$^n$ | math.CV | We construct automorphisms of $\C^n$ which map certain discrete sequences one
onto another with prescribed finite jet at each point, thus solving a general
Mittag-Leffler interpolation problem for automorphisms. Under certain
circumstances, this can be done while also approximating a given automorphism
on a compact set... | math |
755 | On the defect of an analytic disc | math.CV | Although the concept of defect of an analytic disc attached to a generic
manifold of $\C^{n}$ seems to play a merely technical role, it turns out to be
a rather deep and fruitful notion for the extendability of CR functions defined
on the manifold.
In this paper we give a new geometric description of defect, drawing
... | math |
756 | Defect and evaluations | math.CV | Let $S$ be a generic submanifold of $C^N$ of real codimension m. In this work
we continue the study, carried over by various authors, of the set of analytic
discs attached to S. Let $M$ be the set of analytic discs attached to $S.$
Given $q \in S$ let $M_q$ be the set of discs $\phi$ in M such that $\phi_(1).$
B. Trepr... | math |
757 | On totally real spheres in complex space | math.CV | We shall prove that there are totally real and real analytic embeddings of
$S^k$ in $\cc^n$ which are not biholomorphically equivalent if $k\geq 5$ and
$n=k+2[\frac{k-1}{4}]$. We also show that a smooth manifold $M$ admits a
totally real immersion in $\cc^n$ with a trivial complex normal bundle if and
only if the compl... | math |
758 | On the boundary orbit accumulation set for a domain with non-compact automorphism group | math.CV | For a smoothly bounded pseudoconvex domain $D\subset{\Bbb C}^n$ of finite
type with non-compact holomorphic automorphism group $\text{Aut}(D)$, we show
that the set $S(D)$ of all boundary accumulation points for $\text{Aut}(D)$ is
a compact subset of $\partial D$ and, if $S(D)$ contains at least three points,
it is con... | math |
759 | A Carleman type theorem for proper holomorphic embeddings | math.CV | In 1927, Carleman showed that a continuous, complex-valued function on the
real line can be approximated in the Whitney topology by an entire function
restricted to the real line. In this paper, we prove a similar result for
proper holomorphic embeddings. Namely, we show that a proper $\cC^r$ embedding
of the real line... | math |
760 | Fuchsian Groups, Quasiconformal Groups, and Conical Limit Sets | math.CV | We construct examples showing that the normalized Lebesgue measure of the
conical limit set of a uniformly quasiconformal group acting discontinuously on
the disc may take any value between zero and one. This is in contrast to the
cases of Fuchsian groups acting on the disc, conformal groups acting
discontinuously on t... | math |
761 | Generalized Bergmann Metrics and Invariance of Plurigenera | math.CV | An invariant kernel for the pluricanonical system of a projective manifold of
general type is introduced. Using this kernel we prove that the Yau volume form
on a smooth projective variety has seminegative Ricci curvature. As a biproduct
we prove the invariance of plurigenera for smooth projective deformations of
manif... | math |
762 | Finitely smooth Reinhardt domains with non-compact automorphism group | math.CV | We give a complete description of bounded Reinhardt domains of finite
boundary smoothness that have non-compact automorphism group. As part of this
program, we show that the classification of domains with non-compact
automorphism group and having only finite boundary smoothness is considerably
more complicated than the... | math |
763 | Singularities of the Bergman kernel for certain weakly pseudoconvex domains | math.CV | Consider the Bergman kernel $K^B(z)$ of the domain $\ellip = \{z \in \Comp^n
; \sum_{j=1}^n |z_j|^{2m_j}<1 \}$, where $m=(m_1,\ldots,m_n) \in \Natl^n$ and
$m_n \neq 1$. Let $z^0 \in \partial \ellip$ be any weakly pseudoconvex point,
$k \in \Natl$ the degenerate rank of the Levi form at $z^0$. An explicit
formula for $K... | math |
764 | Bohr's power series theorem in several variables | math.CV | Generalizing a classical one-variable theorem of Harald Bohr, we show that if
an n-variable power series has modulus less than 1 in the unit polydisc, then
the sum of the moduli of the terms is less than 1 in the polydisc of radius
1/(3*n^{1/2}). | math |
765 | Breakdown of analyticity for d-bar-b and Szego kernels | math.CV | The CR manifold M_m = { Im z_2= Re z_1^{2m} } (m=2,3,...) is the
counterexample, which has been given by M. Christ and D. Geller, to analytic
hypoellipticity of d-bar-b and real analyticity of the Szego kernel. In order
to give a direct interpretation for the breakdown of real analyticity of the
Szego kernel, we give a... | math |
766 | The dbar-Neumann problem in the Sobolev topology | math.CV | revision posted November 1996 | math |
767 | Gleason's problem in weighted Bergman space on egg domains | math.CV | In the paper, we discuss on the egg domains: $$
\Omega_a=\left\{\xi=(z,w)\in\bold C^{n+m}: \ z\in\bold C^n, \ w\in\bold C^m,
|z|^2+|w|^{2/a}<1\right\}, \qquad 0<a\le 2. $$ We show that Gleason's problem
can be solved in the weight Bergman space on theegg domains. The proof will
need the help of the recent work of the s... | math |
768 | Effective formulas for invariant functions -- case of elementary Reinhardt domains | math.CV | In the paper we find effective formulas for the invariant functions,
appearing in the theory of several complex variables, of the elementary
Reinhardt domains. This gives us the first example of a large family of domains
for which the functions are calculated explicitly. | math |
769 | Sampling sets for Hardy spaces of the disk | math.CV | We propose two possible definitions for the notion of a sampling sequence (or
set) for Hardy spaces of the disk. The first one is inspired by recent work of
Bruna, Nicolau, and \O yma about interpolating sequences in the same spaces,
and it yields sampling sets which do not depend on the value of $p$ and
correspond to ... | math |
770 | Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in C^2 | math.CV | In this paper we give an asymptotic expansion of the Bergman kernel for
certain weakly pseudoconvex tube domains of finite type in C^2. Our asymptotic
formula asserts that the singularity of the Bergman kernel at weakly
pseudoconvex points is essentially expressed by using two variables; moreover
certain real blowing-u... | math |
771 | Sharp Lipschitz estimates for operator dbar_M on a q-concave CR manifold | math.CV | We prove that the integral operators $R_r$ and $H_r$ constructed in \cite{P}
and such that $$f = \bar\partial_{\bold M} R_r(f) + R_{r+1}(\bar\partial_{\bold
M} f) + H_r(f),$$ for a differential form $f \in C_{(0,r)}^{\infty}({\bold M})$
on a regular q-concave CR manifold ${\bold M}$ admit sharp estimates in the
Lipschi... | math |
772 | Defects for Ample Divisors of Abelian Varieties, Schwarz Lemma, and Hyperbolic Hypersurfaces of Low Degrees | math.CV | The main purpose of this paper is to prove the following theorem on the
defect relations for ample divisors of abelian varieties.
Main Theorem. Let $A$ be an abelian variety of complex dimension $n$ and $D$
be an ample divisor in $A$. Let $f:{\bf C}\rightarrow A$ be a holomorphic map.
Then the defect for the map $f$ ... | math |
773 | Hyperbolic Reinhardt Domains in C^2 with Noncompact Automorphism Group | math.CV | We give an explicit description of hyperbolic Reinhardt domains D in C^2 such
that: (i) D has C^k-smooth boundary for some k greater than or equal to 1, (ii)
D intersects at least one of the coordinate complex lines $\{z_1=0\}$,
$\{z_2=0\}$, and (iii) D has noncompact automorphism group. We also give an
example that ex... | math |
774 | The involutive structure on the blow-up of R^n in C^n | math.CV | We investigate the natural involutive structure on the blow-up of ${\Bbb
R}^n$ in ${\Bbb C}^n$ extending the complex structure on the complement of the
exceptional hypersurface. Our main result is that this structure is
hypocomplex, meaning that any solution is locally a holomorphic function of a
basic set of independe... | math |
775 | Application of the Complex Monge-Ampere equation to the study of proper holomorphic mappings of strictly pseudoconvex domains | math.CV | We construct a special plurisubharmonic defining function for a smoothly
bounded strictly pseudoconvex domain so that the determinant of the complex
Hessian vanishes to high order on the boundary. This construction, coupled with
regularity of solutions of complex Monge-Ampere equation and the reflection
principle, enab... | math |
776 | $\overline{\partial}$-Neumann Problem in the Sobolev Topology | math.CV | We study the $\overline{\partial}$-Neumann problem using the Sobolev space
inner product. We show that the problem can be solved on any smoothly bounded,
pseudoconvex domain. We further formulate estimates and the basic results of a
Sobolev Hodge theory. | math |
777 | Domains with Non-Compact Automorphism Group: A Survey | math.CV | We survey results arising from the study of domains in C^n with non-compact
automorphism group. Beginning with a well-known characterization of the unit
ball, we develop ideas toward a consideration of weakly pseudoconvex (and even
non-pseudoconvex) domains with particular emphasis on characterizations of (i)
smoothly ... | math |
778 | The Julia-Wolff-Caratheodory theorem in polydisks | math.CV | The classical Julia-Wolff-Caratheodory theorem gives a condition ensuring the
existence of the non-tangential limit of both a bounded holomorphic function
and its derivative at a given boundary point of the unit disk in the complex
plane. This theorem has been generalized by Rudin to holomorphic maps between
unit balls... | math |
779 | Global regularity of the dbar-Neumann problem: a survey of the L^2-Sobolev theory | math.CV | This is a survey article written for the proceedings of the special year in
several complex variables, 1995-1996, at the Mathematical Sciences Research
Institute in Berkeley. | math |
780 | Plurisubharmonic functions and subellipticity of the dbar-Neumann problem on nonsmooth domains | math.CV | We show subellipticity of the d-bar Neumann problem on domains with Lipschitz
boundary in the presence of plurisubharmonic functions with Hessians of
algebraic growth. In particular, a subelliptic estimate holds near a point
where the boundary is piecewise smooth of finite type. | math |
781 | Parametrization of local biholomorphisms of real analytic hypersurfaces | math.CV | Let $M$ be a real analytic hypersurface in $\bC^N$ which is finitely
nondegenerate, a notion that can be viewed as a generalization of Levi
nondegenerate, at $p_0\in M$. We show that if $M'$ is another such hypersurface
and $p'_0\in M'$, then the set of germs at $p_0$ of biholomorphisms $H$ with
$H(M)\subset M'$ and $H... | math |
782 | Blow-analytic retraction onto the central fibre | math.CV | Let X be a complex analytic space and let f:X -> C be a proper complex
analytic function with nonsingular generic fibres. By adapting the blowanalytic
methods of Kuo we construct a retraction of a neighbourhood of the central
fibre f^{-1}(0) onto f^{-1}(0). Our retraction is defined by the flow of a real
analytic vecto... | math |
783 | Positivity conditions for bihomogeneous polynomials | math.CV | In this paper we continue our study of a complex variables version of
Hilbert's seventeenth problem by generalizing some of the results from [CD].
Given a bihomogeneous polynomial $f$ of several complex variables that is
positive away from the origin, we proved that there is an integer $d$ so that
$||z||^{2d} f(z,{\ove... | math |
784 | Multiplicity of a zero of an analytic function on a trajectory of a vector field | math.CV | Let P(x) be a germ at the origin of an analytic function in C^n, where x =
(x_1,..., x_n), and let
\xi = \xi_1(x) d/dx_1 + ... + \xi_n(x) d/dx_n
be a germ at the origin of an analytic vector field. Suppose that \xi(0) !=
0, and let \gamma be a trajectory of \xi through the origin. Suppose that
P|_\gamma /\equiv 0, ... | math |
785 | On the Lojasiewicz exponent of the gradient of a polynomial function | math.CV | Let h = \sum h_{\alpha \beta} X^\alpha Y^\beta be a polynomial with complex
coefficients. The Lojasiewicz exponent of the gradient of h at infinity is the
upper bound of the set of all real \lambda such that |grad h(x, y)| >=
c|(x,y)|^\lambda in a neighbourhood of infinity in C^2, for c > 0. We estimate
this quantity i... | math |
786 | Factorization of proper holomorphic mappings through Thullen Domains | math.CV | In this article, we consider a bounded pseudoconvex domain in ${\bf C}^2$
satifying:
(a) it admits a proper holomorphic mapping $f$ onto the unit ball $B^2$, and
(b) it is simply connected and has a real analytic boundary.
According to [Barletta-Bedford, Indiana U. Math. J, 39(1985), 315-338], the
strong pseudcon... | math |
787 | Extension Properties of Meromorphic Mappings with Values in Non-Kahler Manifolds | math.CV | We prove an analogue of E. Levi's Continuity Principle for meromorphic
mappings with values in arbitrary compact complex manifolds in place of the
Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new
extension method for meromorphic mappings. One of the corollaries reads as
follows:
If a compact com... | math |
788 | Normal forms and biholomorphic equivalence of real hypersurfaces in C^3 | math.CV | We consider the problem of describing the local biholomorphic equivalence
class of a real-analytic hypersurface $M$ at a distinguished point $p_0\in M$
by giving a normal form for such objects. In order for the normal form to carry
useful information about the biholomorphic equivalence class, we shall require
that the ... | math |
789 | Optimal regularity for d-bar-b on CR manifolds | math.CV | In this paper a new explicit integral formula is derived for solutions of the
tangential Cauchy-Riemann equations on CR q-concave manifolds and optimal
estimates in the Lipschitz norms are obtained. | math |
790 | Some applications of the Kohn-Rossi extension theorems | math.CV | We prove extension results for meromorphic functions by combining the
Kohn-Rossi extension theorems with Andreotti's theory on the algebraic and
analytic dependence of meromorphic functions on pseudoconcave manifolds.
Versions of Kohn-Rossi theorems for pseudoconvex domains are included. | math |
791 | The football player and the infinite series | math.CV | This is the text of an expository talk given at the May 1997 Detroit meeting
of the American Mathematical Society. It is a tale of a famous football player
and a subtle problem he posed about the uniform convergence of Dirichlet
series. Hiding in the background is the theory of analytic functions of an
infinite number ... | math |
792 | Zeta-functions for germs of meromorphic functions and Newton diagrams | math.CV | For a germ of a meromorphic function f=P/Q, we offer notions of the monodromy
operators at zero and at infinity. If the holomorphic functions P and Q are
non-degenerated with respect to their Newton diagrams, we give an analogue of
the formula of Varchenko for the zeta-functions of these monodromy operators. | math |
793 | Ordinary differential equations with only entire solutions | math.CV | We prove necessary and sufficient conditions for a system $\dot
z_i=z_ip_i(z)$ ($p_i$ a polynomial) to have only entire analytic functions as
solutions. | math |
794 | The Bergman kernel function: explicit formulas and zeroes | math.CV | We show how to compute the Bergman kernel functions of some special domains
in a simple way. As an application of the explicit formulas, we show that the
Bergman kernel functions of some convex domains, for instance the domain in C^3
defined by the inequality |z_1|+|z_2|+|z_3|<1, have zeroes. | math |
795 | On the Lojasiewicz exponent at infinity for polynomial functions | math.CV | The Lojasiewicz exponent at infinity of an entire function measures of the
infimal rate of growth of its gradient. The authors compute the Lojasiewicz
exponents at infinity of the 3-variable complex polynomials
x - 3 x^{2n+1} y^{2q} + 2 x^{3n+1} y^{3q} + y z | math |
796 | Holomorphic factorization of matrices of polynomials | math.CV | This paper considers some work done by the author and Catlin [CD1,CD2,CD3]
concerning positivity conditions for bihomogeneous polynomials and metrics on
bundles over certain complex manifolds. It presents a simpler proof of a
special case of the main result in [CD3], providing also a self-contained proof
of a generaliz... | math |
797 | On a domain in C^2 with generic piecewise smooth Levi-flat boundary and non-compact automorphism group | math.CV | In this paper, we prove that if D is a simply-connected domain in C^2 with
generic piecewise smooth Levi-flat boundary and non-compact automorphism group,
then D is biholomorphic to the bidisc. The proof is based on a careful analysis
of invariant measures. | math |
798 | Compactness of the d-bar-Neumann problem on convex domains | math.CV | The d-bar-Neumann operator on (0,q)-forms ($1\le q \le n$) on a bounded
convex domain Omega in C^n is compact if and only if the boundary of Omega
contains no complex analytic (equivalently: affine) variety of dimension
greater than or equal to q. | math |
799 | Finite interpolation with minimum uniform norm in C^n | math.CV | Given a finite sequence $a:={a_1, ..., a_N}$ in a domain $\Omega \subset
C^n$, and complex scalars $v:={v_1, ..., v_N}$, consider the classical extremal
problem of finding the smallest uniform norm of a holomorphic function
verifying $f(a_j)=v_j$ for all $j$. We show that the modulus of the solutions
to this problem mu... | math |
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