Perelmanʼs W-entropy for the Fokker–Planck equation over complete Riemannian manifolds |
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| Authors: | Xiang-Dong Li |
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| Institution: | Academy of Mathematics and System Science, Chinese Academy of Sciences, 55, Zhongguancun East Road, Beijing, 100190, PR China;LMA, CNRS UMR 6086;Institut de Mathématiques de Bourgogne;IRMA, Université de Strasbourg |
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| Abstract: | We establish a monotonicity theorem and a rigidity theorem for the Perelman W-entropy of the Fokker–Planck equation on complete Riemannian manifolds with non-negative m-dimensional Bakry–Emery Ricci curvature. Moreover, we give a probabilistic and kinetic interpretation of the W-entropy for the Fokker–Planck equation on complete Riemannian manifolds. |
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