Multi-K-bi-Lipschitz equivalence in dimension two

被引：0

作者：

Birbrair, Lev ^{[1
]}

Mendes, Rodrigo ^{[2
,3
]}

机构：

[1] Univ Fed Ceara UFC, Dept Matemat, Campus Pici Bloco 914, BR-60455760 Fortaleza, CE, Brazil

[2] Univ Integracao Int Lusofonia Afro Brasileira UNIL, Inst Ciencias Exatas & Nat, Campus Palmares, BR-62785000 Acarape, CE, Brazil

[3] Ben Gurion Univ Negev, Dept Math, POB 653, IL-84105 Beer Sheva, Israel

来源：

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | 2024年 / 18卷 / 02期

关键词：

Width; Lipschitz Geometry; Contact equivalence; Singularity; Semialgebraic sets;

D O I：

10.1007/s40863-024-00404-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study Multi-K-equivalence of multi-germs of functions on the plane, definable in a polynomially bounded o-minimal structure. As in Birbrair et al. (Annali SNS Pisa 17:81-92, 2017. https://doi.org/10.2422/2036-2145.201503_014), we partition the germ of the plane at origin into zones of arcs in such a way that it produces a non-Archimedean space (set of orders and width functions) compatible with a given multi-germ, encoding its asymptotic behaviour. Such a partition is called Multi-pizza. We show the existence, uniqueness and complete invariance of multi-pizzas with respect to the Multi-K-bi-Lipschitz equivalence.

引用

页码：1165 / 1177

页数：13

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