Sur la rigidité de polyèdres hyperboliques en dimension 3 : cas de volume fini, cas hyperidéal, cas fuchsien
Mathias Rousset
Abstract
A hyperbolic semi-ideal polyedron is a polyedron whose vertices lie inside the hyperbolic space H3 or at infinity. A hyperideal polyedron is, in the projective model, the intersection of H3 with a projective polyhedron whose vertices all lie outside of H3, and whose edges all meet H3. We classify semi-ideal polyhedra in terms of their dual metric, using the results of Rivin and Hodgson in comp et idea. This result is used to obtain the classification of hyperideal polyhedra in terms of their combinatorial type and their dihedral angles. These two results are generalized to the case of fuchsian polyhedra.
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