Calculus of Variations and Geometric Measure Theory

F. Essebei - E. Pasqualetto

Variational problems concerning sub-Finsler metrics in Carnot groups

created by pasqualetto on 18 Feb 2022
modified by essebei on 15 Apr 2023


Published Paper

Inserted: 18 feb 2022
Last Updated: 15 apr 2023

Journal: ESAIM: Control, Optimisation and Calculus of Variations
Pages: 31
Year: 2022

ArXiv: 2202.08634 PDF


This paper is devoted to the study of geodesic distances defined on a subdomain of a given Carnot group, which are bounded both from above and from below by fixed multiples of the Carnot-Carath\'{e}odory distance. We show that the uniform convergence (on compact sets) of these distances can be equivalently characterized in terms of $\Gamma$-convergence of several kinds of variational problems. Moreover, we investigate the relation between the class of intrinsic distances, their metric derivatives and the sub-Finsler convex metrics defined on the horizontal bundle.

Keywords: Gamma-convergence, Carnot group, Induced intrinsic distance, sub-Finsler metric