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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 λ1(Γ\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.
Received: 2007-10-09
Published Online: 2009-06-16
Published in Print: 2009-July
© Walter de Gruyter Berlin · New York 2009
