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Conformal Geometry and Dynamics

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Compact Klein surfaces of genus $5$ with a unique extremal disc

Author: Gou Nakamura
Journal: Conform. Geom. Dyn. 17 (2013), 39-46
MSC (2010): Primary 30F50; Secondary 05C10
Published electronically: February 28, 2013
MathSciNet review: 3027523
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Abstract: A compact (orientable or non-orientable) surface of genus $g$ is said to be extremal if it contains an extremal disc, that is, a disc of the largest radius determined only by $g$. The present paper concerns non-orientable extremal surfaces of genus $5$. We represent the surfaces as side-pairing patterns of a hyperbolic regular $24$-gon, that is, a generic fundamental region of an NEC group uniformizing each of the surfaces. We also describe the group of automorphisms of the surfaces with a unique extremal disc.

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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

Received by editor(s): April 16, 2012
Published electronically: February 28, 2013
Additional Notes: This work was supported by Grant-in-Aid for Young Scientists (B) (No. 20740081), Japan Society for the Promotion of Science.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.