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On interpolation and curvature via Wasserstein geodesics.
- Source :
-
Advances in Calculus of Variations . Apr2017, Vol. 10 Issue 2, p125-167. 43p. - Publication Year :
- 2017
-
Abstract
- In this article, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel-Brascamp-Lieb inequality for general Riemannian and Finsler manifolds and led Lott-Villani and Sturm to define an abstract Ricci curvature condition. Following their ideas, a similar condition can be defined and for positively curved spaces one can prove a Poincaré inequality. Using Gigli's recently developed calculus on metric measure spaces, even a q-Laplacian comparison theorem holds on q-infinitesimal convex spaces. In the appendix, the theory of Orlicz-Wasserstein spaces is developed and necessary adjustments to prove the interpolation inequality along geodesics in those spaces are given. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 18648258
- Volume :
- 10
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Advances in Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 122464532
- Full Text :
- https://doi.org/10.1515/acv-2014-0040