lean/docs/091.md

Logarithmic and L_p Brunn–Minkowski inequalities and the B-conjecture

The following describes the scope of the Lean formalization related to the following accompanying paper(s):

• The logarithmic Brunn–Minkowski conjecture

Scope

The logarithmic Brunn–Minkowski conjecture asserts that logarithmic interpolation of origin-symmetric convex bodies preserves the geometric-mean lower bound for volume. The formalized result proves, for every dimension $n\ge1$, such bodies $K,L\subset\mathbb R^n$, and $0\le t\le1$, that their logarithmic Wulff combination has volume at least $|K|^{1-t}|L|^t$. It assumes neither boundary smoothness nor coordinatewise unconditionality.

Comparator links

Result	Comparator statement
Logarithmic Brunn–Minkowski inequality	LogBrunnMinkowski.lean