Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

Ivan Gentil

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arXiv · 1310.4264

Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold

Ivan Gentil

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Abstract

We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a compact Riemannian manifold taking account of the dimension. The result generalizes in a Riemannian context, the dimensional contraction established in [BGG13] for the Euclidean heat equation. It is proved by using a dimensional coercive estimate for the Hodge-de Rham semigroup on 1-forms.

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Ivan Gentil. 2013-10-16. Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold. https://arxiv.org/abs/1310.4264

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