Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity

created by resende on 27 Apr 2022

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Submitted Paper

Inserted: 27 apr 2022
Last Updated: 27 apr 2022

Year: 2022

ArXiv: 2204.11947 PDF
In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d area minimizing currents, beyond that, several results are stated in the more general context of $(C_0,\alpha_0,r_0)$-almost area minimizing currents of arbitrary dimension m and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes one-sided and two-sided points, of any 2d area minimizing current $T$ is an open dense set in $\Gamma$.