2008/06/02 by Mese, Chikako, Yamada, Sumio · 1 citation
#32S25 #35J20 (Secondary) #53A10 #53A30 (Primary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0806.0278
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.