Mathematics – Differential Geometry
Scientific paper
2008-06-02
Mathematics
Differential Geometry
22pages, 1figure, arguments modified
Scientific paper
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.
Mese Chikako
Yamada Sumio
No associations
LandOfFree
Local uniformization and free boundary regularity of minimal singular surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Local uniformization and free boundary regularity of minimal singular surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local uniformization and free boundary regularity of minimal singular surfaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-631616