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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.

Jun 5, 2013
Jun 17, 2013

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