The Logarithmic Sobolev and Sobolev Inequalities Along the Ricci Flow

被引：25
|
作者：
Ye, Rugang [1 ]
机构：
[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
来源：
COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2015年 / 3卷 / 01期
关键词：
Sobolev inequality; Logarithmic Sobolev inequality; Ricci flow; Heat operator;
D O I：
10.1007/s40304-015-0046-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Based on Perelman's entropy monotonicity, uniform logarithmic Sobolev inequalities along the Ricci flow are derived. Then uniform Sobolev inequalities along the Ricci flow are derived via harmonic analysis of the integral transform of the relevant heat operator. These inequalities are fundamental analytic properties of the Ricci flow. They are also extended to the volume-normalized Ricci flow and the Kahler-Ricci flow.
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页码：1 / 36
页数：36
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