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On the number of optimal surfaces
Alina Vdovina
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Geometry & Topology Monographs 14
(2008) 557–567
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Abstract
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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.
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To the memory of Heiner
Zieschang
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Keywords
optimal surface, hyperbolic structure,
maximal embedded disk, minimal covering disk
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Mathematical Subject Classification
Primary: 53C20
Secondary: 20H10, 53C40
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Publication
Received: 31 July 2006
Revised: 28 July 2007
Accepted: 28 July 2007
Published: 29 April 2008
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