TitleUniqueness of boundary tangent cones for $2$-dimensional area-minimizing currents
Publication TypeMagazine Article
Year of Publication2021
AuthorsDe Lellis C, Nardulli S, Steinbruechel S
Type of ArticleBoundary

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].