English

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 nn-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

R2 v1 2026-06-28T10:49:15.534Z