Calculus of Variations and Geometric Measure Theory

C. De Lellis - S. Nardulli - S. Steinbruechel

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

created by delellis on 07 Nov 2021



Inserted: 7 nov 2021
Last Updated: 7 nov 2021

Year: 2021


In this paper we show that, if $T$ is an area-minimizing $2$-dimensional integral current with $\partial T = Q \llbracket \Gamma \rrbracket$, where $\Gamma$ is a $C^{1,\alpha}$ curve for $\alpha>0$ and $Q$ an arbitrary integer, then $T$ 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.