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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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Compact non-orientable surfaces of genus 6 with extremal metric discs
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by Gou Nakamura
Conform. Geom. Dyn. 20 (2016), 218-234
DOI: https://doi.org/10.1090/ecgd/298
Published electronically: June 20, 2016

Abstract:

A compact hyperbolic surface of genus $g$ is said to be extremal if it admits an extremal disc, a disc of the largest radius determined only by $g$. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for $g=3, 4, 5$, or $g>6$. We show that non-orientable extremal surfaces of genus 6 admit at most two extremal discs. The locus of extremal discs is also obtained for each surface. Consequently non-orientable extremal surfaces of arbitrary genus $g\geqq 3$ admit at most two extremal discs. Furthermore we determine the groups of automorphisms of non-orientable extremal surfaces of genus 6 with two extremal discs.
References
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Bibliographic Information
  • Gou Nakamura
  • Affiliation: Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-Cho Toyota 470-0392, Japan
  • MR Author ID: 639802
  • Email: gou@aitech.ac.jp
  • Received by editor(s): October 10, 2015
  • Received by editor(s) in revised form: February 17, 2016
  • Published electronically: June 20, 2016
  • Additional Notes: This work was partially supported by the JSPS KAKENHI Grant No. 25400147.

  • Dedicated: Dedicated to Professor Noriaki Suzuki on the occasion of his sixtieth birthday
  • © Copyright 2016 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 20 (2016), 218-234
  • MSC (2010): Primary 30F50; Secondary 30F40, 05C10
  • DOI: https://doi.org/10.1090/ecgd/298
  • MathSciNet review: 3513567