Regularity of area minimizing currents III: blow-up

Abstract

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.

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Authors

Camillo De Lellis

Mathematik Institut der Universität Zürich, Switzerland

Emanuele Spadaro

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