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

2024/08/02 by Toshizumi Fukui, Fukui, Toshizumi, Masaru Hasegawa +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2408.13258

Abstract

We describe singularities of height 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 dual surfaces of such singular surfaces.

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