5 papers
Existence and uniqueness theorem for convex polyhedral metrics on compact surfaces
François Fillastre
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface can be realized as a convex polyh…
Gauss images of hyperbolic cusps with convex polyhedral boundary
François Fillastre, Ivan Izmestiev
We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone s…
Polyhedral hyperbolic metrics on surfaces
François Fillastre
In the last section of \cite{CompHyp} it is proved that the map is a finite-sheeted covering map between and . As is simply c…
Fuchsian polyhedra in Lorentzian space-forms
François Fillastre
Let S be a compact surface of genus >1, and g be a metric on S of constant curvature K\in\{-1,0,1\} with conical singularities of negative singular curvature. When K=1 we add the c…
Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces
François Fillastre
A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invarian…