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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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:March 2016
Deposited On:10 Aug 2016 08:25
Last Modified:08 Dec 2017 19:55
Publisher:Mathematical Sciences Publishers
ISSN:0003-486X
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4007/annals.2016.183.2.2

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