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Convex Hulls in the Hyperbolic Space

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arxiv 1105.6017 v2 pith:7K73RW2Z submitted 2011-05-30 math.MG math.DG

Itai Benjamini , Ronen Eldan This is my paper · ORCID
classification math.MGmath.DG
keywords hyperbolicconstantconvexexistspointssmallerspacethere
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We show that there exists a universal constant C>0 such that the convex hull of any N points in the hyperbolic space H^n is of volume smaller than C N, and that for any dimension n there exists a constant C_n > 0 such that for any subset A of H^n, Vol(Conv(A_1)) < C_n Vol(A_1) where A_1 is the set of points of hyperbolic distance to A smaller than 1.

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