Eigenvalue monotonicity for the Ricci-Hamilton flow

被引：42

作者：

Ma, Li ^{[1
]}

机构：

[1] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2006年 / 29卷 / 03期

关键词：

Ricci-Hamilton flow; eigenvalue; monotonicity;

D O I：

10.1007/s10455-006-9018-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this short note, we discuss the monotonicity of the eigen-values of the Laplacian operator to the Ricci-Hamilton flow on a compact or a complete non-compact Riemannian manifold. We show that the eigenvalue of the Lapacian operator on a compact domain associated with the evolving Ricci flow is non-decreasing provided the scalar curvature having a non-negative lower bound and Einstein tensor being not too negative. This result will be useful in the study of blow-up models of the Ricci-Hamilton flow.

引用

页码：287 / 292

页数：6