Geometric & Functional Analysis GAFA

, Volume 3, Issue 6, pp 564–631 | Cite as

Reimann surfaces with shortest geodesic of maximal length

  • P. Schmutz
Article

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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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • P. Schmutz
    • 1
  1. 1.Mathematisches InstitutETH-ZentrumZürichSwitzerland

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