An upper bound on the growth of Dirichlet tilings of hyperbolic spaces

Itai Benjamini; Tsachik Gelander

doi:10.1142/S1793525317500030

An upper bound on the growth of Dirichlet tilings of hyperbolic spaces

Itai Benjamini, Tsachik Gelander

Department of Mathematics

Weizmann Institute of Science

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

Abstract

It is shown that the growth rate (lim(r) |B(r)|(1/r)) of any k faces Dirichlet tiling of H-d, d > 2, is at most k - 1 - epsilon, for an epsilon > 0, depending only on k and d. We do not know if there is a universal epsilon(u) > 0, such that k - 1 - epsilon(u) upperbounds the growth rate for any k- regular tiling, when d >2>

Original language	English
Pages (from-to)	221-224
Number of pages	4
Journal	Journal of Topology and Analysis
Volume	9
Issue number	2
DOIs	https://doi.org/10.1142/S1793525317500030
State	Published - Jun 2017

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1142/S1793525317500030

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An upper bound on the growth of Dirichlet tilings of hyperbolic spaces

Abstract

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