Title | The fine structure of the singular set of area-minimizing integral currents III: Frequency 1 flat singular points and H^{m-2}-a.e uniqueness of tangent cones |

Publication Type | Journal Article |

Year of Publication | 2023 |

Authors | De Lellis C, Minter P, Skorobogatova A |

Type of Article | Interior regularity |

Abstract | We consider an area-minimizing integral current $T$ of codimension higher than $1$ in a smooth Riemannian manifold $\Sigma$. We prove that $T$ has a unique tangent cone, which is a superposition of planes, at $\mathcal{H}^{m-2}$-a.e. point in its support. In combination with works of the first and third authors, we conclude that the singular set of $T$ is countably $(m-2)$-rectifiable. The techniques in the present work can be seen as a counterpart for area-minimizers, in arbitrary codimension, to those developed by Simon ([29]) for multiplicity one classes of minimal surfaces and Wickramasekera ([32]) for stable minimal hypersurfaces. |

Notes | Preprint |

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