Uniqueness of boundary tangent cones for $2$-dimensional area-minimizing currents
Camillo De Lellis, Stefano Nardulli, Simone Steinbrüchel · arXiv (Cornell University) · 2021
In this paper we show that, if $T$ is an area-minimizing $2$-dimensional integral current with $\partial T = Q [\![ Γ]\!]$, where $Γ$ is a $C^{1,α}$ curve for $α>0$ 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.