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

2015/04/15 by Fang, Yangqin
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.03861

Abstract

In [15], Jean Taylor has proved a regularity theorem away from boundary for Almgren almost minimal sets of dimension two in ℝ³. 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 ℝ³. It will be of use for understanding their boundary behavior.

Related

• Local C^1,β-regularity at the boundary of two dimensional sliding almost minimal sets in ℝ³
• Sliding almost minimal sets and the Plateau problem
• Hölder Regularity of Two-Dimensional Almost-Minimal Sets in \Rⁿ
• A local description of 2-dimensional almost minimal sets bounded by a curve
• Local regularity properties of almost- and quasiminimal sets with a sliding boundary condition