On bi-Lipschitz invariance and the uniqueness of tangent cones
Journal of Singularities, Tome 25 (2022), pp. 393-402
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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.
@article{10_5427_jsing_2022_25s,
author = {J. Edson Sampaio and E. Carvalho da Silva},
title = {On {bi-Lipschitz} invariance and the uniqueness of tangent cones},
journal = {Journal of Singularities},
pages = {393--402},
publisher = {mathdoc},
volume = {25},
year = {2022},
doi = {10.5427/jsing.2022.25s},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25s/}
}
TY - JOUR AU - J. Edson Sampaio AU - E. Carvalho da Silva TI - On bi-Lipschitz invariance and the uniqueness of tangent cones JO - Journal of Singularities PY - 2022 SP - 393 EP - 402 VL - 25 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25s/ DO - 10.5427/jsing.2022.25s ID - 10_5427_jsing_2022_25s ER -
%0 Journal Article %A J. Edson Sampaio %A E. Carvalho da Silva %T On bi-Lipschitz invariance and the uniqueness of tangent cones %J Journal of Singularities %D 2022 %P 393-402 %V 25 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25s/ %R 10.5427/jsing.2022.25s %F 10_5427_jsing_2022_25s
J. Edson Sampaio; E. Carvalho da Silva. On bi-Lipschitz invariance and the uniqueness of tangent cones. Journal of Singularities, Tome 25 (2022), pp. 393-402. doi: 10.5427/jsing.2022.25s
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