Rotational symmetry of self-similar solutions to the Ricci flow

被引：95

作者：

Brendle, Simon ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

INVENTIONES MATHEMATICAE | 2013年 / 194卷 / 03期

基金：

美国国家科学基金会;

关键词：

CURVATURE; SOLITONS; 3-MANIFOLDS; UNIQUENESS;

D O I：

10.1007/s00222-013-0457-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.

引用

页码：731 / 764

页数：34

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