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

DOI10.1016/J.NA.2023.113235arXiv2111.02981MaRDI QIDQ6382229

S. Nardulli, Simone Steinbrüchel, Camillo De Lellis

Publication date: 4 November 2021

Abstract: In this paper we show that, if $T$ is an area-minimizing $2$-dimensional integral current with $partialT=Q[![Gamma]!]$, 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.

Mathematics Subject Classification ID

Real- or complex-valued set functions (28A10) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

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