Triangulations of uniform subquadratic growth are quasi-trees release_2vzew5ytgzg73octgcxmh2awee

by Itai Benjamini, Agelos Georgakopoulos

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2022  

Abstract

It is known that for every α≥ 1 there is a planar triangulation in which every ball of radius r has size Θ(r^α). We prove that for α <2 every such triangulation is quasi-isometric to a tree. The result extends to Riemannian 2-manifolds of finite genus, and to large-scale-simply-connected graphs. We also prove that every planar triangulation of asymptotic dimension 1 is quasi-isometric to a tree.
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Type  article
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Date   2022-05-26
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Language   en ?
arXiv  2106.06443v2
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