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Riemann surfaces with longest systole and an improved Voronoï algorithm

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Published in Archiv der Mathematik. 2001, vol. 76, no. 3, p. 231 - 240
Abstract In this paper we introduce a new method in order to find the Riemann surface M of a fixed topological type with the longest systole; it is based on a cell decomposition of the Teichmüller space of M. The method also works in the Euclidean case and is similar to the so-called Voronoï algorithm for positive definite quadratic forms, or equivalently, for lattice sphere packings. In particular, we give a new proof of Rogers' theorem.
Stable URL https://archive-ouverte.unige.ch/unige:12384
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Deposited on : 2010-11-09

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