Regularity of area minimizing currents II: center manifold

Camillo De Lellis and Emanuele Spadaro

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Submission date: 05. Jun. 2013
Pages: 56
published in: Annals of mathematics, 183 (2016) 2, p. 499-575 
DOI number (of the published article): 10.4007/annals.2016.183.2.2
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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 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.