OPEN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE RICCI CURVATURE AND LARGE VOLUME GROWTH

被引：4

作者：

Zhang, Yuntao ^{[1
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 143卷 / 11期

关键词：

Ricci curvature; finite topological type; volume growth; THEOREM;

D O I：

10.1090/proc12787

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume growth conditions. We also generalize it to the manifolds with kth asymptotically nonnegative Ricci curvature by using extensions of Abresch-Gromoll's excess function estimate.

引用

页码：4913 / 4923

页数：11

共 15 条

[1]

ABRESCH U, 1985, ANN SCI ECOLE NORM S, V18, P651

[2]

Abresch Uwe, 1990, J AM MATH SOC, V3, P355, DOI DOI 10.1090/S0894-0347-1990-1030656-6

[3] Open manifolds with asymptotically nonnegative curvature [J].

Bazanfare, Mahaman .

ILLINOIS JOURNAL OF MATHEMATICS, 2005, 49 (03) :705-717

[4]

CHEEGER J, 1991, LECT NOTES MATH, V1504, P1

[5]

Grove K., 1993, P S PURE MATH, V54

[6] Complete manifolds with asymptotically nonnegative Ricci curvature and weak bounded geometry [J].

Hu, Zisheng ;

Xu, Senlin .

ARCHIV DER MATHEMATIK, 2007, 88 (05) :455-467

[7]

Mahaman B., 2008, ARXIV08094558

[8]

Shen Z., 1993, P S PURE MATH, V54.3, P539, DOI 10.1090/pspum/054.3/1216645

[9] ON COMPLETE MANIFOLDS OF NONNEGATIVE KTH-RICCI CURVATURE [J].

SHEN, ZM .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 338 (01) :289-310

[10] Complete manifolds with nonnegative Ricci curvature and large volume growth [J].

Shen, ZM .

INVENTIONES MATHEMATICAE, 1996, 125 (03) :393-404

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