Relative volume comparison with integral curvature bounds

被引：127

作者：

Petersen, P ^{[1
]}

Wei, G

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 1997年 / 7卷 / 06期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s000390050036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we shall generalize the Bishop-Gromov relative volume comparison estimate to a situation where one only has an integral bound for the part of the Ricci curvature which lies below a given number. This will yield several compactness and pinching theorems.

引用

页码：1031 / 1045

页数：15

共 6 条

[1] CONVERGENCE AND RIGIDITY OF MANIFOLDS UNDER RICCI CURVATURE BOUNDS [J].

ANDERSON, MT .

INVENTIONES MATHEMATICAE, 1990, 102 (02) :429-445

[2]

Anderson MT., 1991, Geom. Funct. Anal, V1, P231, DOI [DOI 10.1007/BF01896203, 10.1007/BF01896203]

[3] SPECTRAL GEOMETRY IN DIMENSION-3 [J].

BROOKS, R ;

PERRY, P ;

PETERSEN, P .

ACTA MATHEMATICA, 1994, 173 (02) :283-305

[4]

GALLOT S, 1988, ASTERISQUE, P191

[5]

Petersen P., 1997, MATH SCI RES I PUBL, V30, P167, DOI DOI 10.2977/PRIMS/1195166127.MR1452874

[6]

YANG D, 1992, ANN SCI ECOLE NORM S, V25, P77

← 1 →