Ends of locally symmetric spaces with maximal bottom spectrum

Lizhen Ji, Peter Li, Jiaping Wang

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let X be a symmetric space of non-compact type and Γ\X a locally symmetric space. Then the bottom spectrum λ1(Γ\X) satisfies the inequality λ1(Γ\X) ≦λ1(X). We show that if equality λ 1(⌈\X) = λ1(X) holds, then Γ\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, Γ\X is isometric to ℝ1×N endowed with a multi-warped metric, where N is compact.

Original languageEnglish (US)
Pages (from-to)1-35
Number of pages35
JournalJournal fur die Reine und Angewandte Mathematik
Issue number632
DOIs
StatePublished - Jul 2009

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