## Checking atomicity of conformal ending measures for Kleinian groups

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- by Kurt Falk, Katsuhiko Matsuzaki and Bernd O. Stratmann PDF
- Conform. Geom. Dyn.
**14**(2010), 167-183 Request permission

## 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.## References

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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
- 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 - © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**14**(2010), 167-183 - MSC (2010): Primary 30F40, 37F35; Secondary 37F30, 28A80
- DOI: https://doi.org/10.1090/S1088-4173-2010-00209-2
- MathSciNet review: 2660143