Smooth Approximations of Quasispheres
Metric Geometry
2025-04-10 v2 Complex Variables
Abstract
We prove that every quasisphere is the Gromov-Hausdorff limit of a sequence of locally smooth uniform quasispheres. We also prove an analogous result in the bi-Lipschitz setting. This extends recent results of D. Ntalampekos from dimension 2 to arbitrary dimension. In the process, we replace the second half of his argument by a completely different, more efficient approach, which should be applicable to other problems.
Cite
@article{arxiv.2503.09253,
title = {Smooth Approximations of Quasispheres},
author = {Spencer Cattalani},
journal= {arXiv preprint arXiv:2503.09253},
year = {2025}
}
Comments
8 pages; improved exposition