Title | Uniqueness of boundary tangent cones for $2$-dimensional area-minimizing currents |

Publication Type | Magazine Article |

Year of Publication | 2021 |

Authors | De Lellis C, Nardulli S, Steinbruechel S |

Type of Article | Boundary |

Abstract | In this paper we show that, if $T$ is an area-minimizing $2$-dimensional integral current with $\partial T = Q \a{\Gamma}$, where $\Gamma$ is a $C^{1,\alpha}$ curve for $\alpha>0$ and $Q$ an arbitrary integer, then $T$ has a unique tangent cone at every boundary point, with a polynomial convergence rate. The proof is a simple reduction to the case $Q=1$, studied by Hirsch and Marini in [8]. |

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