  Plateau's problem is to show the existence of an area minimizing surface with
a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by
Plateau showed that an area minimizing surface can be obtained in the form of a
film of oil stretched on a wire frame, and the problem came to be called
Plateau's problem. Special cases have been solved by Douglas, Rado,
Besicovitch, Federer and Fleming, and others. Federer and Fleming used the
chain complex of integral currents with its continuous boundary operator to
solve Plateau's problem for orientable, embedded surfaces. But integral
currents cannot represent surfaces such as the Moebius strip or surfaces with
triple junctions. In the class of varifolds, there are no existence theorems
for a general Plateau problem because of a lack of a boundary operator. We use
the chain complex of differential chains with its continuous boundary operator
to solve a general version of Plateau's problem. We find the first solution
which minimizes area taken from a collection of surfaces that includes all
previous special cases, as well as all smoothly immersed surfaces of any genus
type, both orientable and nonorientable, and surfaces with multiple junctions.
  Our result holds for all dimensions and codimensions in (\R^n).
