Checking atomicity of conformal ending measures for Kleinian groups

Falk, Kurt; Matsuzaki, Katsuhiko; Stratmann, Bernd

doi:10.1090/S1088-4173-2010-00209-2

Checking atomicity of conformal ending measures for Kleinian groups
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by Kurt Falk, Katsuhiko Matsuzaki and Bernd O. Stratmann

Conform. Geom. Dyn. 14 (2010), 167-183

DOI: https://doi.org/10.1090/S1088-4173-2010-00209-2

Published electronically: June 30, 2010

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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.

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