Finsler currents
arXiv:2305.18095 · doi:10.1007/s00526-024-02882-7
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.
21 pages; to appear in Calculus of Variations and Partial Differential Equations