Distance squared functions on singular surfaces parameterized by smooth maps A-equivalent to S_k, B_k, C_k and F₄

2024/08/01 by Toshizumi Fukui, Fukui, Toshizumi, Masaru Hasegawa +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Functional Equations Stability Results #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.2408.00231

openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe singularities of distance squared functions on singular surfaces in ℝ³ parameterized by smooth map-germs A-equivalent to one of S_k, B_k, C_k and F₄ singularities in terms of extended geometric language via finite succession of blowing-ups. We investigate singularities of wave-fronts and caustics of such singular surfaces.

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