Kazhdan's property (T), L2-spectrum and isoperimetric inequalities for locally symmetric spaces
Kazhdan's property (T), L2-spectrum and isoperimetric inequalities for locally symmetric spaces
Let V =\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) …