2018/10/12 by A. A. Ardentov, Ardentov, A., Enrico Le Donne +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Elasticity and Material Modeling #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1810.05431
openalex publication_date 2018/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler ℓ_∞ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.