Local uniformization and free boundary regularity of minimal singular surfaces
Abstract
In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free boundary curve. The free boundary is the singular set along which three disk-type minimal surfaces meet. Here the configuration of the singular minimal surface is obtained by a minimization of a weighted energy functional, in the spirit of J.Douglas' approach to the Plateau Problem. Using the free boundary regularity of the harmonic map, we construct a local uniformization of the singular surface as a parameterization of a neighborhood of a point on the free boundary by the singular tangent cone. In addition, applications of the local uniformization are discussed in relation to H.Lewy's real analytic extension of minimal surfaces.
Cite
@article{arxiv.0806.0278,
title = {Local uniformization and free boundary regularity of minimal singular surfaces},
author = {Chikako Mese and Sumio Yamada},
journal= {arXiv preprint arXiv:0806.0278},
year = {2008}
}
Comments
22pages, 1figure, arguments modified