Regularity of area minimizing currents III: blow-up


This is the last of a series of three papers in which we give a new, shorter proof of a slightly improved version of Almgren’s partial regularity of area minimizing currents in Riemannian manifolds. Here we perform a blow-up analysis deducing the regularity of area minimizing currents from that of Dir-minimizing multiple valued functions.


Camillo De Lellis

Mathematik Institut der Universität Zürich, Switzerland

Emanuele Spadaro

Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany