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math.MG2023
Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces
François Fillastre, Roman Prosanov
We first prove that given a hyperbolic metric on a closed surface , any flat metric on with negative singular curvatures isometrically embeds as a convex polyhedral Cauc…
math.MG2015
Hyperbolization of cusps with convex boundary
François Fillastre, Ivan Izmestiev, Giona Veronelli
We prove that for every metric on the torus with curvature bounded from below by -1 in the sense of Alexandrov there exists a hyperbolic cusp with convex boundary such that the ind…
math.MG2003★ 10 cited
From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston
Francois Fillastre
After work of W. P. Thurston, C. Bavard and É. Ghys constructed particular hyperbolic polyhedra from spaces of deformations of Euclidean polygons. We present this construction as a…