Title | Regularity theory for 2-dimensional almost minimal currents I: Lipschitz approximation |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | De Lellis C., Spadaro E., Spolaor L. |

Journal | Transactions of the American Mathematical Society |

Volume | 370 |

Pagination | 1783–1801 |

Publisher | American Mathematical Society |

Type of Article | Interior regularity |

ISSN | 0002-9947 |

Abstract | We construct Lipschitz Q-valued functions which carefully approximate integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the discreteness of the singular set for the following three classes of 2-dimensional integral currents: area minimizing in Riemannian manifolds, semicalibrated and spherical cross sections of 3-dimensional area minimizing cones. |

Notes | Trans. Amer. Math. Soc. 370 (2018), no. 3, 1783–1801 |

URL | https://www.ams.org/journals/tran/2018-370-03/S0002-9947-2017-06995-6/ |

DOI | 10.1090/tran/6995 |

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