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

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.

13 pages, 3 figures

References in corpus (1)

• Unimodal generalized pseudo-Anosov maps