Discrete groups and holomorphic functions

Abstract

We determine conditions under which the quotient of a Kahler-Hadamard manifold by a torsion-free, discrete group of isometries admits a big set of nontrivial holomorphic functions. We also generalize a theorem of G. A. Margulis on centerless of cocompact discrete groups of automorphisms of a Caratheodory hyperbolic manifold by a different approach based on the Caratheodory pseudodistance.