Abstract
In this paper, we will give a C 1 , β C^{1,\beta } -regularity result on the boundary for two dimensional sliding almost minimal sets in R 3 \mathbb {R}^3 . This effect may apply to the regularity of the soap films at the boundary, and may also lead to the existence of a solution to the Plateau problem with sliding boundary conditions proposed by Guy David in the case that the boundary is a 2-dimensional smooth submanifold.
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