Convex hulls in the hyperbolic space

Itai Benjamini; Ronen Eldan

doi:10.1007/s10711-011-9687-8

Convex hulls in the hyperbolic space

Itai Benjamini, Ronen Eldan

Weizmann Institute of Science, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the convex hull of any N points in the hyperbolic space ℍ ⁿ is of volume smaller than 2(2√π) ⁿ/Γ(n/2)N and that for any dimension n there exists a constant C _n > 0 such that for any set A ⊂ ℍ ⁿwhere A ₁ is the set of points of hyperbolic distance to A smaller than 1.

Original language	English
Pages (from-to)	365-371
Number of pages	7
Journal	Geometriae Dedicata
Volume	160
Issue number	1
DOIs	https://doi.org/10.1007/s10711-011-9687-8
State	Published - Oct 2012

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/s10711-011-9687-8

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title = "Convex hulls in the hyperbolic space",

abstract = "We show that the convex hull of any N points in the hyperbolic space ℍ n is of volume smaller than 2(2√π) n/Γ(n/2)N and that for any dimension n there exists a constant C n > 0 such that for any set A ⊂ ℍ nwhere A 1 is the set of points of hyperbolic distance to A smaller than 1.",

author = "Itai Benjamini and Ronen Eldan",

note = "Israel Science Foundation; Farajun Foundation FellowshipPartially supported by the Israel Science Foundation and by a Farajun Foundation Fellowship.",

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Convex hulls in the hyperbolic space

Abstract

All Science Journal Classification (ASJC) codes

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