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arXiv · 2312.06938

The Lipschitz type of the Geometric Directional Bundle

Satoshi Koike·Laurentiu Paunescu
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Abstract

In this paper we investigate the behaviour of the geometric directional bundles, associated to arbitrary subsets in R^n, under bi-Lipschitz homeomorphisms, and give conditions under which their bi-Lipschitz type is preserved. The most general sets we consider satisfy the sequence selection property (SSP) and, consequently, we investigate the behaviour of such sets under bi-Lipschitz homeomorphisms as well. In particular, we show that the bi-Lipschitz images of a subanalytic sets generically satisfy the (SSP) property.

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Satoshi Koike, Laurentiu Paunescu. 2023-12-12. The Lipschitz type of the Geometric Directional Bundle. https://arxiv.org/abs/2312.06938

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