【摘 要】
：
In this talk,we will first review Perelman's W-entropy formula for Ricci flow and the W-entropy formula for the heat equation of the Witten Laplacian on com
【机 构】
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Academy of Mathematics and Systems Science,Chinese Academy of Sciences,China
【出 处】
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The 11th Workshop on Markov Processes and Related topics(第十一
论文部分内容阅读
In this talk,we will first review Perelman's W-entropy formula for Ricci flow and the W-entropy formula for the heat equation of the Witten Laplacian on complete Riemannian manifolds.Then we will introduce the W-entropy and prove the W-entropy formula for the geodesic flow on the Wasserstein space(i.e.,the optimal transport problem)over Riemannian manifolds.To explain the similarity between these two W-entropy formulas,we will introduce a deformation of geometric flows on the Wasserstein space,which interpolates the geodesic flow on the Wasserstein space and the heat equation of the Witten Laplacian on the underlying manifold.Finally,we will prove the W-entropy type formula for each geometric flow in the above deformation on the Wasserstein space.
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