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arXiv · 0806.0278

Local uniformization and free boundary regularity of minimal singular surfaces

Chikako Mese·Sumio Yamada
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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.

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Chikako Mese, Sumio Yamada. 2008-09-24. Local uniformization and free boundary regularity of minimal singular surfaces. https://arxiv.org/abs/0806.0278

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