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Plateau’s problem in Finsler 3-space

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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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  1. Institut für Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany

    Patrick Overath & Heiko von der Mosel

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  1. Patrick Overath
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Overath, P., von der Mosel, H. Plateau’s problem in Finsler 3-space. manuscripta math. 143, 273–316 (2014). https://doi.org/10.1007/s00229-013-0626-x

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