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Polyhedral hyperbolic metrics on surfaces

Fillastre, François

In: Geometriae Dedicata, 2008, vol. 134, no. 1, p. 177-196

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    Title
    • Polyhedral hyperbolic metrics on surfaces
    Author
    • Fillastre, François. Department of Mathematics, University of Fribourg, Pérolles, Chemin du Musée 23, 1700, Fribourg, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:319368
    Summary
    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