On the number of optimal surfaces
Geometric Topology
2009-04-14 v1 Metric Geometry
Abstract
Let X be a closed oriented Riemann surface of genus > 1 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 > 3 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.
Cite
@article{arxiv.0904.1877,
title = {On the number of optimal surfaces},
author = {Alina Vdovina},
journal= {arXiv preprint arXiv:0904.1877},
year = {2009}
}
Comments
This is the version published by Geometry & Topology Monographs on 29 April 2008