  This 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.
