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arXiv · 2304.06610

Multi-$\mathcal{K}$-Lipschitz equivalence in dimension two

Lev Birbrair·Rodrigo Mendes
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Abstract

In this paper, we study Multi-$\mathcal{K}$-equivalence of multi-germs of functions on the plane, definable in a polynomially bounded o-minimal structure. 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 multigerm, encoding its asymptotic behaviour. Such a partition is called Multipizza. We show the existence, uniqueness and complete invariance of Multipizzas with respect to the Multi-$\mathcal{K}$-Lipschitz equivalence.

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Lev Birbrair, Rodrigo Mendes. 2023-04-13. Multi-$\mathcal{K}$-Lipschitz equivalence in dimension two. https://arxiv.org/abs/2304.06610

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