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
收藏
页码：1165 / 1177
页数：13
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