arXiv subjects

Michał Kosiba

Publications and source records attributed to Michał Kosiba.

2 recordsLinked to original sources

arXiv2024

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

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.

math.AG↗

arXiv2023

Generalized Łojasiewicz's inequality for definable and subanalytic multifunctions

This paper is devoted to proving the general Łojasiewicz inequality, in both the definable and subanalytic cases, under the most relaxed assumptions. It means that we drop the usual continuity and compactness assumptions. In the second part of the paper we concentrate on the Łojasiewicz inequality for multifunctions and apply it to the natural multifunctions related to the medial axis of a set (basic notion in pattern recognition).

math.AG↗