TY - JOUR
T1 - Checking atomicity of conformal ending measures for kleinian groups
AU - Falk, Kurt
AU - Matsuzaki, Katsuhiko
AU - Stratmann, Bernd O.
PY - 2010
Y1 - 2010
N2 - 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 nontrivial examples for purely atomic as well as for non-atomic conformal ending measures.
AB - 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 nontrivial examples for purely atomic as well as for non-atomic conformal ending measures.
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U2 - 10.1090/S1088-4173-2010-00209-2
DO - 10.1090/S1088-4173-2010-00209-2
M3 - Article
AN - SCOPUS:77956157537
VL - 14
SP - 167
EP - 183
JO - Conformal Geometry and Dynamics
JF - Conformal Geometry and Dynamics
SN - 1088-4173
ER -