Hamilton differential Harnack inequality and W-entropy for Witten Laplacian on Riemannian manifolds |
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Authors: | Songzi Li Xiang-Dong Li |
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Institution: | 1. School of Mathematical Sciences, Beijing Normal University, No. 19, Xin Jie Kou Wai Da Jie, 100875, China;2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 55, Zhongguancun East Road, Beijing, 100190, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China |
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Abstract: | In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the -condition, where and are two constants. Moreover, we introduce the W-entropy and prove the W-entropy formula for the fundamental solution of the Witten Laplacian on complete Riemannian manifolds with the -condition and on compact manifolds equipped with -super Ricci flows. |
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Keywords: | primary 53C44 58J35 58J65 secondary 60J60 60H30 Hamilton differential Harnack inequality Super Ricci flows |
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