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arXiv · 1810.05431

Sub-Finsler geodesics on the Cartan group

A. Ardentov·E. Le Donne·Yu. Sachkov
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Abstract

This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ 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.

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A. Ardentov, E. Le Donne, Yu. Sachkov. 2018-10-12. Sub-Finsler geodesics on the Cartan group. https://arxiv.org/abs/1810.05431

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