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

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.