On Almgren's center manifold: regularity of minimal surfaces without Schauder

Motivated by the study of Almgren's center manifold in the regularity of higher codimension mass-minimizing currents, I will present a new proof of the higher regularity ($C^{3,\alpha }$) of multiplicity one minimal surfaces without using the non-parametric Schauder's estimates. This is a joint work with C. De Lellis.