Checking atomicity of conformal ending measures for Kleinian groups
Complex Variables
2009-03-20 v1 Dynamical Systems
Abstract
In this paper we address questions of continuity and atomicity of conformal ending measures for arbitrary non-elementary Kleinian groups. We give sufficient conditions under which such ending measures are purely atomic. Moreover, we will show that if a conformal ending measure has an atom which is contained in the big horospherical limit set, then this atom has to be a parabolic fixed point. Also, we give detailed discussions of non-trivial examples for purely atomic as well as for non-atomic conformal ending measures.
Keywords
Cite
@article{arxiv.0903.3332,
title = {Checking atomicity of conformal ending measures for Kleinian groups},
author = {Kurt Falk and Katsuhiko Matsuzaki and Bernd O Stratmann},
journal= {arXiv preprint arXiv:0903.3332},
year = {2009}
}
Comments
20 pages