Escape from compact sets of normal curves in Carnot groups

Enrico Le Donne; Nicola Paddeu

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arXiv · 2304.03205

Escape from compact sets of normal curves in Carnot groups

Enrico Le Donne·Nicola Paddeu

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Abstract

In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, each such a curve leaves every compact set, quantitatively. Namely, the distance between the points at time 0 and time $t$ grows at least of the order of $t^{1/s}$, where $s$ denotes the step of the Carnot group. In particular, in subFinsler Carnot groups there are no periodic normal geodesics.

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BibTeX RIS

Enrico Le Donne, Nicola Paddeu. 2023-04-06. Escape from compact sets of normal curves in Carnot groups. https://arxiv.org/abs/2304.03205

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