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On the number of optimal surfaces

Lookup NU author(s): Dr Alina Vdovina

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Abstract

Let X be a closed oriented Riemann surface of genus ≥ 2 of constant negative curvature -1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus ≥ 4 up to orientation-preserving isometry. We show that the automorphism group of such a surface is always cyclic of order 1, 2, 3 or 6. We also describe a combinatorial structure of nonorientable hyperbolic optimal surfaces.

Publication metadata

Author(s): Vdovina A

Publication type: Article

Publication status: Published

Journal: Geometry and Topology Monographs

Year: 2008

Volume: 14

Pages: 557-567

Date deposited: 27/11/2012

ISSN (print): 1464-8989

ISSN (electronic): 1464-8997

Publisher: Mathematical Sciences Publishers

URL: http://dx.doi.org/10.2140/gtm.2008.14.557

DOI: 10.2140/gtm.2008.14.557

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