Estimate and monotonicity of the first eigenvalue under the Ricci flow

被引：25

作者：

Cao, Xiaodong ^{[1
]}

Hou, Songbo ^{[2
]}

Ling, Jun ^{[3
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[2] China Agr Univ, Dept Appl Math, Coll Sci, Beijing 100083, Peoples R China

[3] Utah Valley Univ, Dept Math, Orem, UT 84058 USA

来源：

MATHEMATISCHE ANNALEN | 2012年 / 354卷 / 02期

基金：

美国国家科学基金会;

关键词：

FUNCTIONALS; LAPLACIAN;

D O I：

10.1007/s00208-011-0740-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first derive a monotonicity formula for the first eigenvalue of on a closed surface with nonnegative scalar curvature under the (unnormalized) Ricci flow. We then derive a general evolution formula for the first eigenvalue under the normalized Ricci flow. As an application, we obtain various monotonicity formulae and estimates for the first eigenvalue on closed surfaces.

引用

页码：451 / 463

页数：13

共 24 条

[1]

[Anonymous], 1971, LECT NOTES MATH, DOI DOI 10.1007/BFB0064643

[2] First eigenvalues of geometric operators under the Ricci flow [J].