An asymptotic theorem for minimal surfaces and existence results for minimal graphs in $H^2 \times R$
| dc.creator | Earp, Ricardo Sa | |
| dc.creator | Toubiana, Eric | |
| dc.date | 2007-12-18 | |
| dc.date.accessioned | 2026-07-07T08:50:03Z | |
| dc.date.available | 2026-07-07T08:50:03Z | |
| dc.description | In this paper we prove a general and sharp Asymptotic Theorem for minimal surfaces in $H^2\times R$. As a consequence, we prove that there is no properly immersed minimal surface whose asymptotic boundary $C$ is a Jordan curve homologous to zero in the asymptotic boundary of $ H^2\times R,$ say $\partial_\infty H^2\times R$, such that $C$ is contained in a slab between two horizontal circles of $\partial_\infty H^2\times R$ with width equal to $π.$ We construct minimal vertical graphs in $H^2\times R$ over certain unbounded admissible domains taking certain prescribed finite boundary data and certain prescribed asymptotic boundary data. Our admissible unbounded domains $\Om$ in $H^2\times \{0\}$ are non necessarily convex and non necessarily bounded by convex arcs; each component of its boundary is properly embedded with zero, one or two points on its asymptotic boundary, satisfying a further geometric condition. | |
| dc.description | This paper was presented in the International Congress on Minimal and Constant Mean Curvature Surfaces, Buzios, Brazil, August 2007 (27 pages 7 figures) | |
| dc.identifier | https://arxiv.org/abs/0712.2972 | |
| dc.identifier | http://arxiv.org/abs/0712.2972 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144488 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42 | |
| dc.title | An asymptotic theorem for minimal surfaces and existence results for minimal graphs in $H^2 \times R$ | |
| dc.type | text |