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.

翻译：我们构造了一个完备的黎曼曲面$Σ$，使得不存在三角剖分$G\subset Σ$满足嵌入映射$G^{(1)} \hookrightarrow Σ$是一个拟等距，其中$G^{(1)}$是$G$的单纯1-骨架。该构造无边界，具有任意大的收缩长度，并且进一步地，不存在任何嵌入图$G\subsetΣ$使得$G^{(1)} \hookrightarrow Σ$是拟等距。这回答了Georgakopoulos提出的一个问题。