arXiv subjects

Maria Ruas

Publications and source records attributed to Maria Ruas.

3 recordsLinked to original sources

arXiv2025

Classification of Lipschitz unimodal function germs

In this paper, we introduce the notion of Lipschitz modality for isolated singularities $ f: (\mathbb{C}^n, 0) \to (\mathbb{C}, 0)$ and provide a complete classification of Lipschitz unimodal singularities of corank~2 with non-zero $4$-jets. As a consequence, such singularities are Lipschitz unimodal if they deform to $J_{10}$ but not to $J_{3,0}$. Furthermore, we show that singularities with vanishing $6$-jets have Lipschitz modality at least~$2$, thus establishing an upper bound for the order of Lipschitz unimodality.

math.AG↗

arXiv2018

Classification of Lipschitz simple function germs

It is known that the bi-Lipschitz right classification of function germs admit moduli. In this article we introduce a notion called the Lipschitz simple function germs and present a full classification in the complex case. A surprising consequence of our result is that a function germ is Lipschitz modal if and only if it deforms to the smooth unimodal family of singularities called $J_{10}$ in Arnold's list.

math.AG↗

arXiv2011

Rigidity of bi-Lipschitz equivalence of weighted homogeneous function-germs in the plane

The main goal of this work is to show that if two weighted homogeneous (but not homogeneous) function-germs $(\C^2,0)\to(\C,0)$ are bi-Lipschitz equivalent, in the sense that these function-germs can be included in a strongly bi-Lipschitz trivial family of weighted homogeneous function-germs, then they are analytically equivalent.

math.AG↗