Plateau's problem in Finsler 3-space
Differential Geometry
2014-01-29 v1 Analysis of PDEs
Classical Analysis and ODEs
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.
Cite
@article{arxiv.1209.2327,
title = {Plateau's problem in Finsler 3-space},
author = {Patrick Overath and Heiko von der Mosel},
journal= {arXiv preprint arXiv:1209.2327},
year = {2014}
}
Comments
42 pages