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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The quasiconformal equivalence of Riemann surfaces and the universal Schottky space
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by Hiroshige Shiga PDF
Conform. Geom. Dyn. 23 (2019), 189-204 Request permission

Abstract:

In the theory of Teichmüller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally equivalent or not. On the other hand, for Riemann surfaces of topologically infinite-type, the situation is rather complicated.

In this paper, after constructing an example which shows the complexity of the problem, we give some geometric conditions for Riemann surfaces to be quasiconformally equivalent.

Our argument enables us to obtain a universal property of the deformation spaces of Schottky regions, which is analogous to the fact that the universal Teichmüller space contains all Teichmüller spaces.

References
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Additional Information
  • Hiroshige Shiga
  • Affiliation: Department of Mathematics, Tokyo Institute of Technology, O-okayama, Meguro-ku Tokyo, Japan
  • Address at time of publication: Department of Mathematics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, Japan
  • MR Author ID: 192109
  • Email: shiga@cc.kyoto-su.ac.jp
  • Received by editor(s): June 28, 2019
  • Received by editor(s) in revised form: July 25, 2019
  • Published electronically: October 30, 2019
  • Additional Notes: The author was partially supported by the Ministry of Education, Science, Sports and Culture, Japan; Grant-in-Aid for Scientific Research (B), 16H03933
  • © Copyright 2019 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 23 (2019), 189-204
  • MSC (2010): Primary 30F60; Secondary 30C62, 30F40
  • DOI: https://doi.org/10.1090/ecgd/343
  • MathSciNet review: 4024932