GC-functions
We prove that for a parabolic subgroup of the fixed points sets of all elements in are the same. This result, together with a deep study of the structure of subgroups of acting freely and properly discontinuously on , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold covered by and such that the group of deck transformations of the covering is “sufficiently generic”, then is isolated in .
We study the growth of parameter-dependent entire functions. We are mainly interested in the case where the functions depend holomorphically on the parameter.