Li-Yau Inequality on Graphs

摘要：

　　We prove the Li-Yau gradient estimate for the heat kernel on graphs.The only assumption is a variant of the curvature-dimension inequality.Moreover, we show that if a graph has nonnegative curvature then it has polynomial volume growth.We also derive Harnack inequalities and heat kernel bounds from the gradient estimate, and show how it can be used to strengthen the classical Buser inequality relating the spectral gap and the Cheeger constant of a graph.This paper is a joint work with Frank Bauer, Paul Horn, Gabor Lippner, Dan Mangoubi and Shing-Tung Yau.

关键词： Curvature-dimension inequality Li-Yau inequality parabolic Harnack inequality heat kernel estimate

作者: Yong Lin

作者单位: DEPARTMENT OF MATHEMATICS, INFORMATION SCHOOL RENMIN UNIVERSITY OF CHINA BEIJING 100872, CHINA

会议类型: 国际会议

会议名称: The 6th International Congress of Chinese Mathematicians (第6届世界华人数学家大会)

会议地点: 台北

会议语种:英文

页码: 445-459

在线出版日期: 2013-07-14（万方平台首次上网日期，不代表论文的发表时间）