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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Checking atomicity of conformal ending measures for Kleinian groups


Authors: Kurt Falk, Katsuhiko Matsuzaki and Bernd O. Stratmann
Journal: Conform. Geom. Dyn. 14 (2010), 167-183
MSC (2010): Primary 30F40, 37F35; Secondary 37F30, 28A80
Published electronically: June 30, 2010
MathSciNet review: 2660143
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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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Additional Information

Kurt Falk
Affiliation: Fachbereich 3 - Mathematik und Informatik, Universität Bremen, Bibliothekstr. 1, D-28359 Bremen, Germany
Email: khf@math.uni-bremen.de

Katsuhiko Matsuzaki
Affiliation: Department of Mathematics, School of Education, Waseda University, Shinjuku, Tokyo 169-8050, Japan
Email: matsuzak@waseda.jp

Bernd O. Stratmann
Affiliation: Fachbereich 3 - Mathematik und Informatik, Universität Bremen, Bibliothekstr. 1, D-28359 Bremen, Germany
Email: bos@math.uni-bremen.de

DOI: http://dx.doi.org/10.1090/S1088-4173-2010-00209-2
PII: S 1088-4173(2010)00209-2
Received by editor(s): March 18, 2009
Published electronically: June 30, 2010
Additional Notes: The first author was supported by the Science Foundation Ireland
The second author was supported by JSPS Grant B #20340030
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.