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arXiv · 1105.6017

Convex Hulls in the Hyperbolic Space

Itai Benjamini·Ronen Eldan
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Abstract

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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Itai Benjamini, Ronen Eldan. 2011-06-02. Convex Hulls in the Hyperbolic Space. https://doi.org/10.1007/s10711-011-9687-8

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