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Communication Dans Un Congrès Current problems in mathematics and mechanics (Sovremennye problemy matematiki i mehaniki) Année : 2011

Existence and uniqueness theorem for convex polyhedral metrics on compact surfaces

Résumé

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a (Riemannian or Lorentzian) space-form. Moreover such a polyhedron is unique, up to global isometries, among convex polyhedra invariant under isometries acting on a totally umbilical surface. This general statement falls apart into 10 different cases. The cases when $S$ is the sphere are classical.
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Dates et versions

hal-00535675 , version 1 (13-11-2010)

Identifiants

  • HAL Id : hal-00535675 , version 1

Citer

François Fillastre. Existence and uniqueness theorem for convex polyhedral metrics on compact surfaces. Conference on metric geometry of surfaces and polyhedra, Dedicated to the 100th anniversary of N. V. Efimov, Aug 2010, Moscou, Russia. pp.208--223. ⟨hal-00535675⟩
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