Convex Hulls in the Hyperbolic Space
Abstract
We show that there exists a universal constant C>0 such that the convex hull of any N points in the hyperbolic space Hn is of volume smaller than C N, and that for any dimension n there exists a constant Cn > 0 such that for any subset A of Hn, Vol(Conv(A1)) < Cn Vol(A1) where A1 is the set of points of hyperbolic distance to A smaller than 1.
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