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COMPACT NON-ORIENTABLE SURFACES OF GENUS 5 WITH EXTREMAL METRIC DISCS

Published online by Cambridge University Press:  12 December 2011

GOU NAKAMURA
GOU NAKAMURA*
Affiliation:
Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-Cho, Toyota 470-0392, Japan e-mail: gou@aitech.ac.jp
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Abstract

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A compact hyperbolic surface of genus g is called an extremal surface if it admits an extremal disc, a disc of the largest radius determined by g. Our problem is to find how many extremal discs are embedded in non-orientable extremal surfaces. It is known that non-orientable extremal surfaces of genus g > 6 contain exactly one extremal disc and that of genus 3 or 4 contain at most two. In the present paper we shall give all the non-orientable extremal surfaces of genus 5, and find the locations of all extremal discs in those surfaces. As a consequence, non-orientable extremal surfaces of genus 5 contain at most two extremal discs.

Keywords

30F5030F40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 273 - 281
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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