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In this paper, we will give a $C^{1,\beta}$-regularity result on the boundaryfor two dimensional sliding almost minimal sets in $\mathbb{R}^3$. This effectmay lead to the existence of a solution to the Plateau problem with slidingboundary conditions proposed by Guy David in \cite{David:2014p} in the casethat the boundary is a 2-dimensional smooth manifold.

Local $C^{1,\beta}$-regularity at the boundary of two dimensional sliding almost minimal sets in $\mathbb{R}^3$