On the number of optimal surfaces
نویسندگان
چکیده
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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تاریخ انتشار 2009