Abstract
I describe Riemann surfaces of constant curvature −1 with the property that the length of its shortest simple closed geodesic is maximal with respect to an open neighborhood in the corresponding Teichmüller space. I give examples of such surfaces. In particular, examples are presented which are modelled upon (Euclidean) polyhedra. This problem is a non-Euclidean analogue of the well known best lattice sphere packing problem.
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Supported by the Schweizerischer Nationalfonds zur Förderung wissenschaftlicher Forschung
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Schmutz, P. Reimann surfaces with shortest geodesic of maximal length. Geometric and Functional Analysis 3, 564–631 (1993). https://doi.org/10.1007/BF01896258
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DOI: https://doi.org/10.1007/BF01896258