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  Finsler currents

Basso, G. (2025). Finsler currents. Calculus of Variations and Partial Differential Equations, 64(1): 21. doi:10.1007/s00526-024-02882-7.

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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 Creators:
Basso, Giuliano1, Author                 
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 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 circumscribed Riemannian and the mass* volume densities.

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Language(s): eng - English
 Dates: 2025
 Publication Status: Issued
 Pages: 20
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 Rev. Type: No review
 Identifiers: arXiv: 2305.18095
DOI: 10.1007/s00526-024-02882-7
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Title: Calculus of Variations and Partial Differential Equations
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 64 (1) Sequence Number: 21 Start / End Page: - Identifier: -