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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

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
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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
Email: gou@aitech.ac.jp

DOI: http://dx.doi.org/10.1090/S1088-4173-2013-00251-8
PII: S 1088-4173(2013)00251-8
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.