Classification of Lipschitz unimodal function germs

2025/10/08 by Nguyen, Nhan, Ruas, Maria, Trivedi, Saurabh
#14B05 #32C05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.06792

Abstract

In this paper, we introduce the notion of Lipschitz modality for isolated singularities f: (ℂⁿ, 0) → (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 J₁₀ 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.

Citations

• A bi-Lipschitz invariant for analytic function germs
• Local quasi-isometries and tangent cones of definable germs
• Lipschitz stratifications in power-bounded o-minimal fields
• Right unimodal and bimodal singularities in positive characteristic

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