Calculus of Variations and Geometric Measure Theory

C. De Lellis - E. Spadaro

Regularity of area-minimizing currents II: center manifold

created by delellis on 02 Jul 2013
modified on 24 May 2017


Published Paper

Inserted: 2 jul 2013
Last Updated: 24 may 2017

Journal: Ann. of Math. (2)
Volume: 183
Pages: 499–575
Year: 2016


This is the second paper of a series of three on the regularity of higher codimension area minimizing integral currents. Here we perform the second main step in the analysis of the singularities, namely the construction of a \textit{center manifold}, i.e.~an approximate average of the sheets of an almost flat area minimizing current. Such center manifold is complemented with a Lipschitz multi-valued map on its normal bundle, which approximates the current with a highe degree of accuracy. In the third and final paper these objects are used to conclude a new proof of Almgren's celebrated dimension bound on the singular set.

Keywords: regularity, area minimizing, Integer rectifiable currents