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In [ 15 ], Jean Taylor proved a regularity theorem away from the boundary for Almgren almost minimal sets of dimension 2 inℝ  3    {\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 inℝ  3    {\mathbb{R}^{3}}   .

Hölder regularity at the boundary of two-dimensional sliding almost minimal sets