On the link of Lipschitz normally embedded sets
Abstract
A path-connected subanalytic subset in is naturally equipped with two metrics: the inner and the outer metrics. We say that a subset is Lipschitz normally embedded (LNE) if these two metrics are equivalent. In this article, we give some criteria for a subanalytic set to be LNE. It is a fundamental question to know if the LNE property is conical, i.e., if it is possible to describe the LNE property of a germ of a subanalytic set in terms of the properties of its link. We answer this question by introducing a new notion called link Lipschitz normally embedding. We prove that this notion is equivalent to the LNE notion in the case of sets with connected links.
Cite
@article{arxiv.2101.05572,
title = {On the link of Lipschitz normally embedded sets},
author = {Rodrigo Mendes and José Edson Sampaio},
journal= {arXiv preprint arXiv:2101.05572},
year = {2023}
}
Comments
The previous version had two sets of different results. We have divided our pre-print into two, and this version contains the first set of results, which was sections 1-4. The second part, which was Section 5, will appear in a new arXiv submission. The title was changed