Preprint

Inserted: 7 nov 2021
Last Updated: 7 nov 2021

Year: 2021

Abstract:

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.

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• UniqTgConesBoundaryCSS1.pdf