Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces

Marcel Vinhas

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arXiv · 2007.08420

Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces

Marcel Vinhas

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Abstract

Given metric quotients $S$ and $S_n$, $n \in \mathbb{N}$, of a metric space $X$, sufficient conditions are provided on the data defining them guaranteeing that $S$ is the Gromov-Hausdorff limit of $S_n$. These conditions are recognized within metric quotients of plane polygons determined by side-pairings known as plain paper-folding schemes. In particular, concrete examples are given of sequences of two-dimensional conic-flat spheres converging to spheres that are conic-flat except around certain singularities, some of them with unbounded curvature in the sense of comparative geometry.

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BibTeX RIS

Marcel Vinhas. 2020-07-16. Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces. https://arxiv.org/abs/2007.08420

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