Geometrically finite groups acting on CAT(-1) spaces

Jeudi 19 mars 2015 14:00-15:00 - David Simmons - Ohio State University

Résumé : In this talk, I will discuss several theorems regarding geometrically finite groups acting on CAT(-1) spaces. The main result is the Global Measure Formula, which estimates the measure of a small ball centered at a point in the limit set, measured with respect to the Patterson-Sullivan measure. The Global Measure Formula is a generalization of a result of Stratmann and Velani (’95) for finite-dimensional real hyperbolic spaces. The main difference is that in a more general setting, there is a much wider range of possible parabolic subgroups, which means that the Global Measure Formula must incorporate functions which describe the behavior of these subgroups. In particular, Patterson-Sullivan measures are no longer necessarily doubling or exact-dimensional ; instead, we give necessary and sufficient conditions for when a Patterson-Sullivan measure is doubling and/or exact-dimensional. We also prove generalizations of Tukia’s isomorphism theorem and Xie’s rigidity theorem. This work is joint with Tushar Das and Mariusz Urbański.

Lieu : bât. 425 - 121-123

Geometrically finite groups acting on CAT(-1) spaces  Version PDF