Local uniformization and free boundary regularity of minimal singular surfaces
| dc.creator | Mese, Chikako | |
| dc.creator | Yamada, Sumio | |
| dc.date | 2008-06-02 | |
| dc.date | 2008-09-24 | |
| dc.date.accessioned | 2026-07-07T10:04:31Z | |
| dc.date.available | 2026-07-07T10:04:31Z | |
| dc.description | 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. | |
| dc.description | 22pages, 1figure, arguments modified | |
| dc.identifier | https://arxiv.org/abs/0806.0278 | |
| dc.identifier | http://arxiv.org/abs/0806.0278 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169708 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53A30 (Primary), 53A10, 32S25, 35J20 (Secondary) | |
| dc.title | Local uniformization and free boundary regularity of minimal singular surfaces | |
| dc.type | text |