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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.

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Bers embedding of the Teichmüller space of a once-punctured torus
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by Yohei Komori and Toshiyuki Sugawa PDF
Conform. Geom. Dyn. 8 (2004), 115-142 Request permission

Abstract:

In this note, we present a method of computing monodromies of projective structures on a once-punctured torus. This leads to an algorithm numerically visualizing the shape of the Bers embedding of a one-dimensional Teichmüller space. As a by-product, the value of the accessory parameter of a four-times punctured sphere will be calculated in a numerical way as well as the generators of a Fuchsian group uniformizing it. Finally, we observe the relation between the Schwarzian differential equation and Heun’s differential equation in this special case.
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Additional Information
  • Yohei Komori
  • Affiliation: Department of Mathematics, Osaka City University, Sugimoto 3-3-138 Sumiyoshi-ku, Osaka, 558-8585 Japan
  • Email: komori@sci.osaka-cu.ac.jp
  • Toshiyuki Sugawa
  • Affiliation: Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526 Japan
  • MR Author ID: 318760
  • Email: sugawa@math.sci.hiroshima-u.ac.jp
  • Received by editor(s): November 6, 2003
  • Received by editor(s) in revised form: March 16, 2004
  • Published electronically: June 8, 2004
  • Additional Notes: The second author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 9740056. A portion of the present research was carried out during the second author’s visit to the University of Helsinki under the exchange program of scientists between the Academy of Finland and the JSPS
  • © Copyright 2004 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 8 (2004), 115-142
  • MSC (2000): Primary 30F60; Secondary 30F40, 34A20
  • DOI: https://doi.org/10.1090/S1088-4173-04-00108-0
  • MathSciNet review: 2060380