Finsler currents
Differential Geometry
2024-12-09 v4 Metric Geometry
Abstract
We propose a slight variant of Ambrosio and Kirchheim's definition of a metric current. We show that with this new definition it is possible to obtain certain volume functionals from Finsler geometry as mass measures of currents. As an application, we obtain a whole family of extendibly convex -volume densities. This family includes the mass* and the circumscribed Riemannian volume densities.
Cite
@article{arxiv.2305.18095,
title = {Finsler currents},
author = {Giuliano Basso},
journal= {arXiv preprint arXiv:2305.18095},
year = {2024}
}
Comments
21 pages; to appear in Calculus of Variations and Partial Differential Equations