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



Inserted: 1 may 2023
Last Updated: 1 may 2023

Year: 2023

ArXiv: 2304.03205 PDF


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