H\"older regularity at the boundary of two-dimensional sliding almost minimal sets

Abstract

In [15], Jean Taylor has proved a regularity theorem away from boundary for Almgren almost minimal sets of dimension two in $\mathbb{R}^{3}$. It is quite important for understanding the soap films and the solutions of Plateau's problem away from boundary. In this paper, we will give a regularity result on the boundary for two dimensional sliding almost minimal sets in $\mathbb{R}^{3}$. It will be of use for understanding their boundary behavior.