Plateau's problem in Finsler 3-space
Patrick Overath, Heiko von der Mosel
TL;DR
This paper investigates Plateau's problem in Finsler 3-space by linking Finslerian area functionals with Cartan functionals, proving regularity of solutions, and addressing boundary problems and isoperimetric inequalities.
Contribution
It introduces a novel approach connecting Finslerian and Cartan functionals to solve Plateau's problem and establishes higher regularity of solutions in Finsler 3-space.
Findings
Established a connection between Finslerian area and Cartan functionals.
Proved higher regularity of solutions to Plateau's problem in Finsler space.
Derived a simple isoperimetric inequality for minimal surfaces in Finsler spaces.
Abstract
We explore a connection between the Finslerian area functional based on the Busemann-Hausdorff-volume form, and well-investigated Cartan functionals to solve Plateau's problem in Finsler 3-space, and prove higher regularity of solutions. Free and semi-free geometric boundary value problems, as well as the Douglas problem in Finsler space can be dealt with in the same way. We also provide a simple isoperimetric inequality for minimal surfaces in Finsler spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.