Triangulations of uniform subquadratic growth are quasi-trees

ITAI BENJAMINI; Agelos Georgakopoulos

doi:10.5802/ahl.139

Triangulations of uniform subquadratic growth are quasi-trees

ITAI BENJAMINI, Agelos Georgakopoulos

Department of Mathematics

Weizmann Institute of Science

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

Abstract

It is known that for every (Formula present) there is a planar triangulation in which every ball of radius r has size (Formula presented). 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.

Original language	English
Pages (from-to)	905-919
Number of pages	15
Journal	Annales Henri Lebesgue
Volume	5
DOIs	https://doi.org/10.5802/ahl.139
State	Published - 2022

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Analysis
Geometry and Topology
Statistics and Probability

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abstract = "It is known that for every (Formula present) there is a planar triangulation in which every ball of radius r has size (Formula presented). 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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AB - It is known that for every (Formula present) there is a planar triangulation in which every ball of radius r has size (Formula presented). 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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M3 - مقالة

VL - 5

SP - 905

EP - 919

JO - Annales Henri Lebesgue

JF - Annales Henri Lebesgue

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Triangulations of uniform subquadratic growth are quasi-trees

Abstract

All Science Journal Classification (ASJC) codes

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