Plateau's problem in Finsler 3-space

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.

42 pages

References in corpus (2)

• A Note on Regularity for the n-dimensional H-System assuming logarithmic higher Integrability
• On minimal immersions in Finsler spaces

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