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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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Cross ratio coordinates for the deformation spaces of a marked Möbius group
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by Kimiyo N. Yamamoto and Masahiko Taniguchi
Conform. Geom. Dyn. 17 (2013), 145-154
DOI: https://doi.org/10.1090/S1088-4173-2013-00259-2
Published electronically: December 30, 2013

Abstract:

We introduce a new kind of coordinate systems for the deformation space of a finitely generated free Möbius group by using cross ratio functions induced by the fixed points of Möbius transformations. As an application, we give a new complete distance on the Schottky space by using such functions, which is not greater than the Teichmüller distance.
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Bibliographic Information
  • Kimiyo N. Yamamoto
  • Affiliation: Department of Information and Computer Sciences, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
  • Email: kimiyo520@gmail.com
  • Masahiko Taniguchi
  • Affiliation: Department of Mathematics, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
  • MR Author ID: 192108
  • Email: tanig@cc.nara-wu.ac.jp
  • Received by editor(s): December 27, 2012
  • Published electronically: December 30, 2013
  • Additional Notes: The first author was supported by JSPS Research Fellowship for Young Scientests (PD) (No. 6811).
    The second author was partially supported by Grant-in-Aid for Scientific Research (C) (Grant No. 23540202) and (B) (Grant No. 25287021).
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 17 (2013), 145-154
  • MSC (2010): Primary 30F40, Secondly, 30F45, 30F60
  • DOI: https://doi.org/10.1090/S1088-4173-2013-00259-2
  • MathSciNet review: 3146812