Hyperideal polyhedra in hyperbolic manifolds
نویسنده
چکیده
Let (M, ∂M) be a 3-manifold with incompressible boundary that admits a convex co-compact hyperbolic metric (but is not a solid torus). We consider the hyperbolic metrics on M such that ∂M looks locally like a hyperideal polyhedron, and we characterize the possible dihedral angles. We find as special cases the results of Bao and Bonahon [BB02] on hyperideal polyhedra, and those of Rousset [Rou02] on fuchsian hyperideal polyhedra. Our results can also be stated in terms of circle configurations on ∂M , they provide an extension of the Koebe theorem on circle packings. The proof uses some elementary properties of the hyperbolic volume, in particular the Schläfli formula and the fact that the volume of (truncated) hyperideal simplices is a concave function of the dihedral angles.
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