Journal
ANNALS OF MATHEMATICS
Volume 183, Issue 2, Pages 499-575Publisher
Princeton Univ, Dept Mathematics
DOI: 10.4007/annals.2016.183.2.2
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Funding
- ERC [ERC 306247]
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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 a center manifold is accompanied by a Lipschitz multivalued map on its normal bundle, which approximates the current with a high degree of accuracy. In the third and final paper these objects are used to conclude the proof of Almgren's celebrated dimension bound on the singular set.
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