One dimensional weighted Ricci curvature and displacement convexity of entropies

Yohei Sakurai

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arXiv · 1706.08225

One dimensional weighted Ricci curvature and displacement convexity of entropies

Yohei Sakurai

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Abstract

In the present paper, we prove that a lower bound on the $1$-weighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the Pr'ekopa-Leindler inequality, the Borel-Branscamp-Lieb inequality, and the Brunn-Minkowski inequality under the curvature bound.

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BibTeX RIS

Yohei Sakurai. 2017-06-26. One dimensional weighted Ricci curvature and displacement convexity of entropies. https://arxiv.org/abs/1706.08225

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