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Triangulations of uniform subquadratic growth are quasi-trees
release_2vzew5ytgzg73octgcxmh2awee
by
Itai Benjamini, Agelos Georgakopoulos
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as a article
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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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2106.06443v2
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