Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case
| dc.creator | Shcherbakova, Nataliya | |
| dc.date | 2007-09-19 | |
| dc.date.accessioned | 2026-07-07T08:30:49Z | |
| dc.date.available | 2026-07-07T08:30:49Z | |
| dc.description | We study minimal surfaces in generic sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called {\it horizontal} area functional associated to the canonical {\it horizontal} area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces in the horizontal spherical bundle over the base manifold. Generic singularities of minimal surfaces turn out the singularities of this projection, and we give a complete local classification of them. We illustrate our results by examples in the Heisenberg group and the group of roto-translations | |
| dc.identifier | https://arxiv.org/abs/0709.2977 | |
| dc.identifier | http://arxiv.org/abs/0709.2977 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138338 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C17, 32S25 | |
| dc.title | Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case | |
| dc.type | text |