Finsler currents

Finsler currents

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 n -vo...

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Veröffentlicht in:Calculus of variations and partial differential equations 2025, Vol.64 (1), Article 21
1. Verfasser: Basso, Giuliano
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
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Zusammenfassung: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 n -volume densities. This family includes the circumscribed Riemannian and the mass* volume densities.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-024-02882-7