Partial regularity of minimizers for real-analytic sub-Riemannian metrics

2018/03/28 by Paolo G. Albano, Albano, Paolo, Antonio Bove +1
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1803.10485

openalex publication_date 2018/03/28 · openalex created_date 2018/04/06 · openalex updated_date 2026/07/28

Abstract

In the real-analytic setting, we show that all sub-Riemannian minimizers (parametrized by the arc-length) are real-analytic everywhere except an at most countable non-dense set. In particular, non-analyticity may occur only on a set of measure zero of the domain of definition of a sub-Riemannian minimizer. Furthermore, we provide a geometrical condition which implies the absence of the so called strictly abnormal minimizers. In particular, under such condition, all sub-Riemannian minimizers (parametrized by the arc-length) are real-analytic.

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