Classification of Lipschitz unimodal function germs

Nhan Nguyen; Maria Ruas; Saurabh Trivedi

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arXiv · 2510.06792

Classification of Lipschitz unimodal function germs

Nhan Nguyen·Maria Ruas·Saurabh Trivedi

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Abstract

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.

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Nhan Nguyen, Maria Ruas, Saurabh Trivedi. 2025-10-08. Classification of Lipschitz unimodal function germs. https://arxiv.org/abs/2510.06792

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