Ends of locally symmetric spaces with maximal bottom spectrum

被引：7

作者：

Ji, Lizhen ^{[1
]}

Li, Peter ^{[2
]}

Wang, Jiaping ^{[3
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[3] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2009年 / 632卷

关键词：

COMPLETE MANIFOLDS; HARMONIC-FUNCTIONS; POSITIVE SPECTRUM; KAHLER-MANIFOLDS; COMPACT; THEOREM;

D O I：

10.1515/CRELLE.2009.048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a symmetric space of non-compact type and Gamma/X a locally symmetric space. Then the bottom spectrum lambda(1)(Gamma\X) satisfies the inequality lambda 1(Gamma\X) <= lambda(1)(X). We show that if equality lambda 1(Gamma\X) = lambda(1)(X) holds, then Gamma/X has either one end, which is necessarily of infinite volume, or two ends, one of infinite volume and another of finite volume. In the latter case, Gamma\X is isometric to R-1 x N endowed with a multi-warped metric, where N is compact.

引用

页码：1 / 35

页数：35

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