English

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.

Keywords

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

R2 v1 2026-06-21T22:03:13.757Z