Year: 2026
Type: preprint
Abstract: We construct a complete Riemannian surface $Σ$ that admits no triangulation $G\subset Σ$ such that the inclusion $G^{(1)} \hookrightarrow Σ$ is a quasi-isometry, where $G^{(1)}$ is the simplicial 1-skeleton of $G$. Our construction is without boundary, has arbitrarily large systole, and furthermore, there is no embedded graph $G\subsetΣ$ such that $G^{(1)} \hookrightarrow Σ$ is a quasi-isometry. This answers a question of Georgakopoulos.
Source: arXiv (Cornell University)
Author: Davies, James
Institution: Leipzig University
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7143542118
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