Lipschitz normally embedded sets do not need to have Lipschitz normally embedded medial axis

2024/03/15 by Michał Kosiba, Kosiba, Michał
Psychology · #14B05 #32B25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Psychotherapy Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2403.10734

openalex publication_date 2024/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study the Lipschitz normally embedded property for a set and its medial axis. We consider if and when a non-LNE set implies non-LNE medial axis and converse. We present an example a of Lipschitz normally set that has medial axis which is not Lipschitz normally emebedded. At the end we discuss special case when a set is a one dimensional germ on a plane.

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