  We show that in the setting of proper metric spaces one obtains a solution of
the classical two-dimensional Plateau problem by minimizing the energy, as in
the classical case, once a definition of area (in the sense of convex geometry)
has been chosen appropriately. We prove the quasi-convexity of this new
definition of area. Under the assumption of a quadratic isoperimetric
inequality we establish regularity results for energy minimizers and improve
Hoelder exponents of some area-minimizing discs.
