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Polyhedral hyperbolic metrics on surfaces

Fillastre, François

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

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,...