Triangulating surfaces quasi-isometrically
Abstract
We prove that if a complete Riemannian surface (Σ,dΣ) is quasi-isometric to some bounded degree graph G, then Σ admits a triangulation whose 1-skeleton is quasi-isometric to it when equipped with the simplicial metric. We study several variants of the problem, and identify the right condition making it an if and only if statement.
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