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MiS Preprint

Regularity of area minimizing currents II: center manifold

Camillo De Lellis and Emanuele Spadaro


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.


Related publications

2016 Repository Open Access
Camillo De Lellis and Emanuele Spadaro

Regularity of area minimizing currents II : center manifold

In: Annals of mathematics, 183 (2016) 2, pp. 499-575