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arXiv · 2111.02981

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

Camillo De Lellis·Stefano Nardulli·Simone Steinbrüchel
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Abstract

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.

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Camillo De Lellis, Stefano Nardulli, Simone Steinbrüchel. 2021-11-04. Uniqueness of boundary tangent cones for $2$-dimensional area-minimizing currents. https://arxiv.org/abs/2111.02981

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