Integral bounds on curvature and Gromov-Hausdorff limits

被引：2

作者：

Chen, X. -X. ^{[1
]}

Donaldson, S. K. ^{[2
]}

机构：

[1] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2BZ, England

来源：

JOURNAL OF TOPOLOGY | 2014年 / 7卷 / 02期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会; 欧洲研究理事会;

关键词：

RICCI CURVATURE; CONVERGENCE; RIGIDITY; SPACES;

D O I：

10.1112/jtopol/jtt037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop a new approach to, and somewhat extend, results of Cheeger, Colding and Tian (Geom. Funct. Anal. 12 (2002) 873-914), which give restrictions on the singular sets that can arise as Gromov-Hausdorff limits in the presence of integral bounds on the curvature. The foundation of this approach is provided by a rigidity result for flat singular spaces, which has independent interest.

引用

页码：543 / 556

页数：14

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