Stability of hyperbolic manifolds with cusps under Ricci flow

被引：14

作者：

Bamler, Richard H. ^{[1
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

ADVANCES IN MATHEMATICS | 2014年 / 263卷

关键词：

Ricci flow; Stability; Hyperbolic manifold; Hyperbolic cusp; Cusp deformation; METRICS; SPACE;

D O I：

10.1016/j.aim.2014.07.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that every finite volume hyperbolic manifold of dimension greater than or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation. It will turn out that the main difficulty in the proof comes from a weak stability of the cusps which has to do with infinitesimal cusp deformations. We will overcome this weak stability by using a new analytical method developed by Koch and Lamm. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：412 / 467

页数：56