Any sub-Riemannian Metric has Points of Smoothness

2008/08/29 by Andrei Agrachev, Agrachev, Andrei · 1 citation
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC) #Point processes and geometric inequalities #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.0808.4059

openalex publication_date 2008/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the result stated in the title; it is equivalent to the existence of a regular point of the sub-Riemannian exponential mapping. We also prove that the metric is analytic on an open everywhere dense subset in the case of a complete real-analytic sub-Riemannian manifold.

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