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ERC Workshop on Optimal Transportation and Applications

Wasserstein Contractions Associated with the Curvature-dimension Condition

speaker: Kazumasa Kuwada (Ochanomizu University)

abstract: We obtain a new characterization of complete Riemannian manifolds with lower Ricci curvature bound and upper dimension bound in terms of the Wasserstein distance between heat distributions. It is formulated as a space-time Lipschitz-type estimate of the Wasserstein distance between two heat distributions with different initial data at different times. It extends a result in the case that no upper dimension bound is imposed. The proof is based on establishing an equivalence with a gradient estimate of heat semigroups studied by F.-Y. Wang. In addition, our new Wasserstein contraction can be obtained by using a coupling method of two Brownian particles with a different speed.

timetable:
Fri 9 Nov, 10:00 - 10:50, Aula Dini
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