Sala Seminari (Dip. Matematica).
I will present a direct approach to solve the the Plateau problem. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of $R^n$: the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. I will also show that the obtained minimizers are regular up to a set of dimension less than (d-1).