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Let X be a symmetric space of non-compact type and Γ\X a locally symmetric space. Then the bottom spectrum λ 1 (Γ\X) satisfies the inequality λ 1 (Γ\X) ≤ λ 1 (X). We show that if equality λ 1 (Γ\X) = λ 1 (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 R 1 × N endowed with a multi-warped metric, where N is compact.doi:10.1515/crelle.2009.048 fatcat:ena7zx3lsbdw7n7xe4qfco6dfu