Regularity of area minimizing currents II: center manifold

• 成果类型: Article
• 署名作者: De Lellis, Camillo; Spadaro, Emanuele
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2016.183.2.2
• 发表日期: 2016
• 页码: 499-575
• 关键词: surfaces

摘要

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.