Regularity of area minimizing currents II: center manifold
Camillo De Lellis and Emanuele Spadaro
Contact the author: Please use for correspondence this email.
Submission date: 05. Jun. 2013
published in: Annals of mathematics, 183 (2016) 2, p. 499-575
DOI number (of the published article): 10.4007/annals.2016.183.2.2
Download full preprint: PDF (689 kB)
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 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.