JournalscmhVol. 78, No. 1pp. 116–133

Kazhdan's property (T), L2L^2-spectrum and isoperimetric inequalities for locally symmetric spaces

  • Enrico Leuzinger

    Karlsruhe Institute of Technology (KIT), Germany
Kazhdan's property (T), $L^2$-spectrum and isoperimetric inequalities for locally symmetric spaces cover
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Abstract

Let V=Γ\G/KV =\Gamma\backslash G/K be a Riemannian locally symmetric space of nonpositive sectional curvature and such that the isometry group G of its universal covering space has Kazhdan's property (T). We establish strong dichotomies between the finite and infinite volume case. In particular, we characterize lattices (or, equivalently, arithmetic groups) among discrete subgroups ΓG\Gamma\subset G in various ways (e.g., in terms of critical exponents, the bottom of the spectrum of the Laplacian and the behaviour of the Brownian motion on V).

Cite this article

Enrico Leuzinger, Kazhdan's property (T), L2L^2-spectrum and isoperimetric inequalities for locally symmetric spaces. Comment. Math. Helv. 78 (2003), no. 1, pp. 116–133

DOI 10.1007/S000140300005