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Journal Articles Potential Analysis Year : 2015

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

Ivan Gentil

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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Dates and versions

hal-00873097 , version 1 (15-10-2013)
hal-00873097 , version 2 (22-05-2014)
hal-00873097 , version 3 (14-12-2014)

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Ivan Gentil. Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold. Potential Analysis, 2015, 52 (4), pp.861-873. ⟨hal-00873097v3⟩
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