| import Mathlib |
| import OAI.Analysis.BiholderTransport.Model |
|
|
| namespace OAI |
|
|
| section |
| section |
| noncomputable section |
| open Set Filter Manifold Bundle Module |
| open scoped Topology ContDiff |
|
|
| namespace WeakMTWTransport |
| section FixedJoinSpectrum |
| variable {n : ℕ} {M : Type*} [MetricSpace M] [ChartedSpace (Model n) M] |
|
|
| local instance tangentFiniteSpectrum (x : M) : |
| FiniteDimensional ℝ (TangentSpace 𝓘(ℝ,Model n) x) := |
| inferInstanceAs (FiniteDimensional ℝ (Model n)) |
|
|
| lemma tangent_finrank (x : M) : finrank ℝ (TangentSpace 𝓘(ℝ,Model n) x)=n := |
| finrank_euclideanSpace_fin |
| end FixedJoinSpectrum |
| end WeakMTWTransport |
|
|
| end |
|
|
| end |
|
|
| section |
|
|
| noncomputable section |
| open Set Filter Manifold Bundle |
| open scoped Topology ContDiff |
|
|
| namespace WeakMTWTransport |
| section EndpointJoinAction |
| variable {n : ℕ} {M : Type*} [MetricSpace M] [CompactSpace M] |
| [ChartedSpace (Model n) M] [IsManifold 𝓘(ℝ,Model n) ∞ M] |
| [RiemannianBundle (fun x : M => TangentSpace 𝓘(ℝ,Model n) x)] |
| [IsContMDiffRiemannianBundle 𝓘(ℝ,Model n) ∞ (Model n) |
| (fun x : M => TangentSpace 𝓘(ℝ,Model n) x)] |
| [IsRiemannianManifold 𝓘(ℝ,Model n) M] |
|
|
| local instance tangentFiniteEndpointJoin (x : M) : |
| FiniteDimensional ℝ (TangentSpace 𝓘(ℝ,Model n) x) := |
| inferInstanceAs (FiniteDimensional ℝ (Model n)) |
| end EndpointJoinAction |
| end WeakMTWTransport |
|
|
| end |
|
|
| end |
|
|
| end |
|
|
| end OAI |
|
|
