| 摘要: |
| 本文研究了黎曼流形上熵幂的凹性问题.利用非线性Bochner公式和Bakry-Émery的方法，证明了当满足曲率维数条件CD（-K，m）（K ≥ 0，m ≥ n）时，对于加权双重扩散方程的正解，相关的p-Rényi熵幂是凹的，推广了之前多孔介质方程以及Ricci曲率非负情形下的结果. |
| 关键词: 凹性 p-Rényi熵幂 加权双重扩散方程 m-Bakry-Émery Ricci曲率 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:Supported by National Natural Science Foundation of China (11701347). |
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| THE CONCAVITY OF p-RÉNYI ENTROPY POWER FOR THE WEIGHTED DOUBLY NONLINEAR DIFFUSION EQUATIONS ON WEIGHTED RIEMANNIAN MANIFOLDS |
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WANG Yu-Zhao, ZHANG Hui-Ting
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School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
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| Abstract: |
| In this paper, we study the concavity of the entropy power on Riemannian manifolds. By using the nonlinear Bochner formula and Bakry-Émery method, we prove p-Rényi entropy power is concave for positive solutions to the weighted doubly nonlinear diffusion equations on the weighted closed Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which generalizes the cases of porous medium equation and nonnegative Ricci curvature. |
| Key words: concavity p-Rényi entropy power weighted doubly nonlinear diffusion equations m-Bakry-Émery Ricci curvature |
