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arXiv · 2603.21189

Triangulating surfaces quasi-isometrically

Agelos Georgakopoulos·Federico Vigolo
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Abstract

We prove that if a complete Riemannian surface $(Σ,d_Σ)$ 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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Agelos Georgakopoulos, Federico Vigolo. 2026-05-16. Triangulating surfaces quasi-isometrically. https://arxiv.org/abs/2603.21189

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