Medial axis detects non-Lipschitz normally embedded points

TL;DR

This paper shows that points where a closed subset of R^n fails to be Lipschitz Normally Embedded are approached by its medial axis, linking geometric properties to medial axis proximity.

Contribution

It establishes a connection between non-Lipschitz normally embedded points and the medial axis in closed subsets of R^n.

Findings

Points not Lipschitz Normally Embedded are approached by the medial axis.

The medial axis characterizes non-Lipschitz normally embedded points.

Abstract

We demonstrate that every point where X - a closed subset of R^n - is not Lipschitz Normally Embedded is approached by the medial axis of X.