Bilipschitz geometry of real surface singularities whose tangent cone is a plane

2024/08/13 by Donal O’Shea, O'Shea, Donal, Leslie C. Wilson +1
Mathematics · #14B05 (Primary) 14J17 #14P10 #51F99 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2408.07218

openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Tangent cones are preserved under ambient bilipschitz equivalence, but the behavior of the Nash cone is more delicate. This paper explores the behavior of the Nash cone and of exceptional rays under ambient bilipschitz equivalence for real surfaces in \mathbb R³ with isolated singularity and whose tangent cone is a plane.

Related

• Exceptional rays and bilipschitz geometry of real surface singularities
• Classifiyng metrically conical rational singularities
• Topological and bilipschitz types of complex surface singularities and their links
• Surfaces of constant curvature in R³ with isolated singularities
• On the exceptional locus of the birational projections of normal surface singularity into a plane