Inserted: 2 jul 2013
Last Updated: 30 sep 2015
Journal: Ann. of Math.
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.
Keywords: regularity, area minimizing, Integer rectifiable currents