Regularity of area minimizing currents II: center manifold

De Lellis, Camillo; Spadaro, Emanuele Nunzio (2016). Regularity of area minimizing currents II: center manifold. Annals of Mathematics. Second Series, 183(2):499-575.

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 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.

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 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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Statistics and Probability Social Sciences & Humanities > Statistics, Probability and Uncertainty English March 2016 10 Aug 2016 08:25 30 Jul 2020 22:08 Mathematical Sciences Publishers 0003-486X Closed Publisher DOI. An embargo period may apply. https://doi.org/10.4007/annals.2016.183.2.2

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