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