  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.
