Rigidity of circle polyhedra in the $2$-sphere and of hyperideal polyhedra in hyperbolic $3$-space
نویسندگان
چکیده
منابع مشابه
Rigidity of Circle Polyhedra in the 2-sphere and of Hyperideal Polyhedra in Hyperbolic 3-space
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 ...
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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 bounded 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 as wel...
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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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2018
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/7483