Calculus of Variations and Geometric Measure Theory

E. Le Donne - N. Paddeu

Escape from compact sets of normal curves in Carnot groups

created by ledonne on 01 May 2023

[BibTeX]

preprint

Inserted: 1 may 2023
Last Updated: 1 may 2023

Year: 2023

ArXiv: 2304.03205 PDF

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.

Tags: GeoMeG