REGULARITY AND PROPERTIES OF THE SINGULAR SET OF PARAMETRIC MINIMAL SURFACES

Abstract

This thesis is mainly about the regularity of parametric minimal surfaces in n-dimensional Euclidean space, and we summarize relevant theorems. The thesis is organized around two key conclusions: the first result is about the analyticity of minimal surfaces for n less equal than 7, and the second one associates with the dimension of the singular set of the boundary of minimal sets. In the thesis, we use Hausdorff measure, minimal cones and other methods to present the proof.