Regularity of higher codimension area minimizing integral currents

Emanuele Spadaro

(MPI Leipzig)

Event: ERC School on Geometric Measure Theory and Real Analysis

Date: Sep 30, 2013

Place: Centro De Giorgi

Abstract. In this series of lectures I will present a new proof of the partial regularity for area minimizing integral currents in any dimension and codimension (obtained in collaboration with C. De Lellis at Zurich), as proven first in Almgren's big regularity paper. After a brief introduction to currents and multiple valued functions, I will focus on the core of the partial regularity results, trying to give a fairly detailed description of the approximation of a current on a center manifold and of the frequency function estimates.