Volume 29, 2023
|Number of page(s)||31|
|Published online||24 March 2023|
Variational problems concerning sub-Finsler metrics in Carnot groups
Dipartimento di Matematica, Università degli Studi di Trento,
Via Sommarive 14,
Povo (Trento), Italy
2 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 11 January 2023
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–Carathéodory distance. We show that the uniform convergence (on compact sets) of these distances can be equivalently characterized in terms of Γ-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.
Mathematics Subject Classification: 53C17 / 49J45 / 51K05
Key words: Carnot group / Gamma-convergence / sub-Finsler metric / induced intrinsic distance
© The authors. Published by EDP Sciences, SMAI 2023
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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