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arXiv 2603.211892026-03math.MG

对表面进行准等距三角剖分

Triangulating surfaces quasi-isometrically

University of Warwick（华威大学）；Georg-August-Universität Göttingen（哥廷根大学）

Agelos Georgakopoulos, Federico Vigolo

备注：: 26 pages, 6 figures. Reorganized the introduction and Section 3

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AI总结：

论文证明了若完备黎曼表面准等距于某种有界度数图，则该表面存在三角剖分，其1骨架在单纯形度量下准等距。研究了多个变体并确定了使其成为充要条件的正确条件。

摘要：

我们证明，若一个完备黎曼表面$(Σ,d_Σ)$准等距于某种有界度数图$G$，则$Σ$存在三角剖分，其1骨架在单纯形度量下准等距。我们研究了该问题的多个变体，并确定了使其成为充要条件的正确条件。

英文摘要：

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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