منابع مشابه
Hyperideal polyhedra in hyperbolic manifolds
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...
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We generalize Cauchy’s celebrated theorem on the global rigidity of convex polyhedra in Euclidean 3-space E to the context of circle polyhedra in the 2-sphere S. We prove that any two convex and proper non-unitary c-polyhedra with Möbiuscongruent faces that are consistently oriented are Möbius-congruent. Our result implies the global rigidity of convex inversive distance circle packings in the ...
متن کاملDirichlet Polyhedra for Cyclic Groups in Complex Hyperbolic Space
We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element y acting on complex hyperbolic «-space centered at an arbitrary point w is bounded by the two hypersurfaces equidistant from the pairs w, yw and w,y~lw respectively. The proof relies on a convexity property of the distance to an isometric flow containing y.
متن کاملOn the Volume of Unbounded Polyhedra in the Hyperbolic Space
In the Euclidean plane the definition of the area of the polygon harmonizes well with intuition, since by the decomposition theorem of Farkas Bolyai [2] two polygons of the same area can be decomposed into pairwise congruent polygons. The definition of the measure of an unbounded polyhedron in twoand in three-dimensional Euclidean space [7] is likewise well-founded, since we obtain an inner cha...
متن کاملNew constructions of fundamental polyhedra in complex hyperbolic space
We give a new construction of fundamental domains in H C for the action of certain lattices in PU(2, 1) defined by Mostow. The polyhedra are given a natural geometric description starting from certain fixed points of elliptic elements. Among the advantages over Dirichlet domains, we gain a simplification of the combinatorics and obtain proofs using mainly synthetic arguments.
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 2002
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.2426