Volume maximization and the extended hyperbolic space
نویسندگان
چکیده
منابع مشابه
Volume Maximization and the Extended Hyperbolic Space
We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We show that critical points of the generalized volume are associated to geometric structures modeled on the extended hyperbolic space – the natural extension o...
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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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Consider a collection of possibly overlapping balls in E d. Suppose the balls are rearranged so that the distances between the centers of the balls all increase or stay the same. Kneser and Poulsen independently conjectured in the 1950’s that the volume of the union must either increase or stay the same. Csikós proved that this is true in Euclidean space under a continuous expansion, and Connel...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-10941-9