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Polyhedral hyperbolic metrics on surfaces

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An Erratum to this article was published on 15 November 2008

Abstract

Let S be a topologically finite surface, and g be a hyperbolic metric on S with a finite number of conical singularities of positive singular curvature, cusps and complete ends of infinite area. We prove that there exists a convex polyhedral surface P in hyperbolic space \({\mathbb{H}^{3}}\) and a group G of isometries of \({\mathbb{H}^{3}}\) such that the induced metric on the quotient P/G is isometric to g. Moreover, the pair (P, G) is unique among a particular class of convex polyhedra.

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  1. Department of Mathematics, University of Fribourg, Pérolles, Chemin du Musée 23, 1700, Fribourg, Switzerland

    François Fillastre

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  1. François Fillastre
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Correspondence to François Fillastre.

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An erratum to this article is available at http://dx.doi.org/10.1007/s10711-008-9305-6.

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Fillastre, F. Polyhedral hyperbolic metrics on surfaces. Geom Dedicata 134, 177–196 (2008). https://doi.org/10.1007/s10711-008-9252-2

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