A Note on the Stability and Uniqueness for Solutions to the Minimal Surface System
| dc.creator | Lee, Yng-Ing | |
| dc.creator | Wang, Mu-Tao | |
| dc.date | 2007-02-11 | |
| dc.date.accessioned | 2026-07-07T07:46:19Z | |
| dc.date.available | 2026-07-07T07:46:19Z | |
| dc.description | In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a minimal submanifold $Σ$ is the graph of a (strictly) distance-decreasing map, then $Σ$ is (strictly) stable. It is known that a minimal graph of codimension one is stable without assuming the distance-decreasing condition. We give another criterion for the stability in terms of the two-Jacobians of the map which in particular covers the codimension one case. All theorems are proved in the more general setting for minimal maps between Riemannian manifolds. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702303 | |
| dc.identifier | http://arxiv.org/abs/math/0702303 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123788 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | A Note on the Stability and Uniqueness for Solutions to the Minimal Surface System | |
| dc.type | text |