The Lipschitz type of the Geometric Directional Bundle

2023/12/12 by Koike, Satoshi, Paunescu, Laurentiu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.06938

Abstract

In this paper we investigate the behaviour of the geometric directional bundles, associated to arbitrary subsets in Rⁿ, 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.

Related

• Stabilisation of geometric directional bundle for a subanalytic set
• On the Geometry of sets satisfying the Sequence Selection Property
• Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones
• The kissing dimension of subanalytic sets is preserved by a bi-Lipschitz homeomorphism
• A Pointwise Lipschitz Selection Theorem