Published Paper
Inserted: 2 jul 2013
Last Updated: 24 may 2017
Journal: Ann. of Math. (2)
Volume: 183
Pages: 499–575
Year: 2016
Abstract:
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
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