Polyhedral hyperbolic metrics on surfaces |
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Authors: | François Fillastre |
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Affiliation: | (1) Department of Mathematics, University of Fribourg, Pérolles, Chemin du Musée 23, 1700 Fribourg, Switzerland |
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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 and a group G of isometries of 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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Keywords: | Hyperbolic generalized polyhedra Equivariant polyhedral realization Complete hyperbolic metrics Alexandrov Theorem Hyperbolic– de Sitter space |
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