Polyhedral hyperbolic metrics on surfaces

Fillastre, François

doi:10.1007/s10711-008-9252-2

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Journal article

Polyhedral hyperbolic metrics on surfaces

Fillastre, François Department of Mathematics, University of Fribourg, Switzerland

18.04.2008

Published in:

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

Hyperbolic generalized polyhedra

Equivariant polyhedral realization

English 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 ℍ³ and a group G of isometries of ℍ³ 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

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language