To appear in J.ReineAng.Math. (Crelles) ENDS OF LOCALLY SYMMETRIC SPACES WITH MAXIMAL BOTTOM SPECTRUM
نویسندگان
چکیده
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. Table of
منابع مشابه
Ends of Locally Symmetric Spaces with Maximal Bottom Spectrum
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 wi...
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