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Dimensional Contraction in Wasserstein Distance for Diffusion Semigroups on a Riemannian Manifold

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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 Bolley et al. J. Lond. Math. Soc. 90(1), 309–332 (2014) 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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  1. Institut Camille Jordan, UMR CNRS 5208, Université Claude Bernard Lyon 1, 43 Boulevard du 11 Novembre 1918, F-69622, Villeurbanne cedex, France

    Ivan Gentil

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  1. Ivan Gentil
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Gentil, I. Dimensional Contraction in Wasserstein Distance for Diffusion Semigroups on a Riemannian Manifold. Potential Anal 42, 861–873 (2015). https://doi.org/10.1007/s11118-015-9460-y

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  • DOI: https://doi.org/10.1007/s11118-015-9460-y

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