Uniqueness of boundary tangent cones for 2-dimensional area-minimizing currents. (May 2023) - De Lellis, Camillo; Nardulli, Stefano; Steinbrüchel, Simone
Abstract: In this paper we show that, if T is an area-minimizing 2-dimensional integral current with ∂ 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 (2019).