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Checking atomicity of conformal ending measures for Kleinian groups
Author(s):
Kurt
Falk;
Katsuhiko
Matsuzaki;
Bernd
O.
Stratmann
Journal:
Conform. Geom. Dyn.
14
(2010),
167-183.
MSC (2010):
Primary 30F40, 37F35;
Secondary 37F30, 28A80
Posted:
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:
10.1090/S1088-4173-2010-00209-2
PII:
S 1088-4173(2010)00209-2
Received by editor(s):
March 18, 2009
Posted:
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 of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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