Title | Regularity of area-minimizing currents II: center manifold |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | De Lellis C., Spadaro E. |

Journal | Annals of Mathematics. Second Series |

Volume | 183 |

Pagination | 499–575 |

Date Published | March |

Publisher | Mathematical Sciences Publishers |

Type of Article | Interior regularity |

ISSN | 0003-486X |

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. |

Notes | Ann. of Math. (2) 183 (2016), no. 2, 499–575. |

URL | http://annals.math.princeton.edu/2016/183-2/p02 |

DOI | 10.4007/annals.2016.183.2.2 |

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