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Asymptotic Estimates on the Time Derivative of Φ-entropy on Riemannian Manifolds

Asymptotic Estimates on the Time Derivative of Φ-entropy on Riemannian Manifolds
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摘要 In this note, we obtain an asymptotic estimate for the time derivative of the O-entropy in terms of the lower bound of the Bakry-Emery F2 curvature. In the cases of hyperbolic space and the Heisenberg group （more generally, the nilpotent Lie group of rank two）, we show that the time derivative of the O-entropy is non-increasing and concave in time t, also we get a sharp asymptotic bound for the time derivative of the entropy in these cases. In this note, we obtain an asymptotic estimate for the time derivative of the O-entropy in terms of the lower bound of the Bakry-Emery F2 curvature. In the cases of hyperbolic space and the Heisenberg group （more generally, the nilpotent Lie group of rank two）, we show that the time derivative of the O-entropy is non-increasing and concave in time t, also we get a sharp asymptotic bound for the time derivative of the entropy in these cases.
作者 Bin QIAN
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第4期609-618,共10页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China(Grant No.11201040)
关键词 Ф-entropy CURVATURE heat kernel hyperbolic space Ф-entropy, curvature, heat kernel, hyperbolic space
分类号 O186.12 [理学—基础数学]
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Acta Mathematica Sinica,English Series
2014年 第4期

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