2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64625This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of math.DG/9810146. Based on this investigation we provide proofs of the Hodge theoretic results for the cohomology of real hyperbolic manifolds announced in math.DG/0009038, improve the bounds for the critical exponents obtained by Corlette for the quaternionic and the Cayley case, compute the L^2-cohomology for the corresponding locally symmetric spaces, prove a version of the Harder-Borel conjecture for real hyperbolic manifolds, and compute higher cohomology groups with coefficients in hyperfunctions supported on the limit set.121 pagesDifferential GeometryRepresentation Theory58J; 22E40; 57R19text