Plateau's problem in Finsler 3-space
Overath, Patrick · von der Mosel, Heiko
Differential Geometry
Analysis of PDEs
Classical Analysis and ODEs
53A35 (Primary), 49Q05, 53B40, 44A12
Original · EN
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.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.