Convex Hulls in the Hyperbolic Space
Metric Geometry
2013-05-21 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1105.6017,
title = {Convex Hulls in the Hyperbolic Space},
author = {Itai Benjamini and Ronen Eldan},
journal= {arXiv preprint arXiv:1105.6017},
year = {2013}
}
Comments
7 pages