• calculus of variations
• gamma-convergence
• geometric measure theory
• metric spaces
• Plateau problems
• rectifiability
• soap films

The characterization problem of higher order rectifiable sets and a modelling problem for soap films are studied. In particular, necessary and sufficient geometric and quantitative conditions for a set to be rectifiable (in a higher order sense) are proved in Euclidean and metric spaces. Furthermore, a soap film model in the Euclidean plane is presented as a way to solving the Plateau problem in the plane.