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arXiv · 1209.2327

Plateau's problem in Finsler 3-space

Patrick Overath·Heiko von der Mosel
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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.

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Patrick Overath, Heiko von der Mosel. 2012-09-11. Plateau's problem in Finsler 3-space. https://doi.org/10.1007/s00229-013-0626-x

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