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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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Compact non-orientable surfaces of genus $4$ with extremal metric discs
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by Gou Nakamura PDF
Conform. Geom. Dyn. 13 (2009), 124-135 Request permission


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 by $g$. We know how many extremal discs are embedded in a non-orientable extremal surface of genus $g=3$ or $g>6$. We show in the present paper that there exist $144$ non-orientable extremal surfaces of genus $4$, and find the locations of all extremal discs in those surfaces. As a result, each surface contains at most two extremal discs. Our methods used here are similar to those in the case of $g=3$.
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Additional 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:
  • Received by editor(s): March 27, 2008
  • Published electronically: April 22, 2009
  • Additional Notes: This work was supported in part by Grant-in-Aid for Young Scientists (B) (No. 20740081).

  • Dedicated: Dedicated to Professor Yoshihiro Mizuta on the occasion of his 60th birthday
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 13 (2009), 124-135
  • MSC (2000): Primary 30F50; Secondary 30F40
  • DOI:
  • MathSciNet review: 2497316