Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 81 | |
Number of page(s) | 18 | |
DOI | https://doi.org/10.1051/cocv/2024067 | |
Published online | 25 October 2024 |
Escape from compact sets of normal curves in subfinsler Carnot groups
University of Fribourg, Chemin du Musée 23, 1700 Fribourg, Switzerland
* Corresponding author: nicola.paddeu@unifr.ch
Received:
21
September
2023
Accepted:
6
September
2024
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 t1/s, where s denotes the step of the Carnot group. In particular, in subFinsler Carnot groups there are no periodic normal geodesics.
Mathematics Subject Classification: 53C17 / 22E25 / 53C22 / 22F30
Key words: Carnot groups / normal curves / periodic geodesics
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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