On bi-Lipschitz invariance and the uniqueness of tangent cones

J. Edson Sampaio and E. Carvalho da Silva

Journal of Singularities
volume 25 (2022), 393-402

Received: 31 March 2021. Received in revised form: 13 May 2021.

DOI: 10.5427/jsing.2022.25s

Add a reference to this article to your citeulike library.

Abstract:

In this note we present some remarks about tangent cones and their invariance under bi-Lipschitz homeomorphisms. In particular, we prove the bi-Lipschitz invariance of tangent cones of sets with unique tangent cone. We obtain also some characterizations for the uniqueness of the tangent cone of a set at a point, for example, the sets which satisfy the sequence selection property (SSP-sets for short) presented by Koike and Paunescu are just those sets which have unique tangent cones. The analogues versions at infinity of these results are also presented.

2010 Mathematical Subject Classification:

32B20; 32B25; 14P10; 14B05

Key words and phrases:

Lipschitz maps, Tangent cone, definable sets, Sequence selection property

Author(s) information:

J. Edson Sampaio
Departamento de Matemática
Universidade Federal do Ceará
Rua Campus do Pici, s/n, Bloco 914, Pici
60440-900, Fortaleza-CE, Brazil
edsonsampaio@mat.ufc.br

E. Carvalho da Silva
Departamento de Matemática
Instituto Federal de Educação
Ciência e Tecnologia do Ceará
Av. Parque Central, 1315, Distrito Industrial I
61939-140, Maracanaú-CE, Brazil
euripedes.carvalho@ifce.edu.br