Compact Klein surfaces of genus 5 with a unique extremal disc

Nakamura, Gou

doi:10.1090/S1088-4173-2013-00251-8

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

Conform. Geom. Dyn. 17 (2013), 39-46

DOI: https://doi.org/10.1090/S1088-4173-2013-00251-8

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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