Adolfo Arroyo-Rabasa is supported by a scholarship from the Hausdorff Center of Mathematics and the University of Bonn; the research conducted in this paper forms part of his Ph.D. thesis at the University of Bonn. Guido De Philippis is supported by the MIUR SIR-grant “Geometric Variational Problems” (RBSI14RVEZ). Filip Rindler acknowledges the support from an EPSRC Research Fellowship on “Singularities in Nonlinear PDEs” (EP/L018934/1).