Minimal surfaces in the Heisenberg group

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dc.creatorPauls, Scott D.
dc.date2001-08-07
dc.date2006-04-13
dc.date.accessioned2026-07-07T06:35:26Z
dc.date.available2026-07-07T06:35:26Z
dc.descriptionWe investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau problem in this setting. Further, we provide a link between our minimal surfaces and Riemannian constant mean curvature surfaces in H equipped with different Riemannian metrics approximating the Carnot-Caratheodory metric. We generate a large library of examples of minimal surfaces and use these to show that the solution to the Dirichlet problem need not be unique. Moreover, we show that the minimal surfaces we construct are in fact X-minimal surfaces in the sense of Garofalo and Nhieu.
dc.description26 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/math/0108048
dc.identifierhttp://arxiv.org/abs/math/0108048
dc.identifierGeom. Ded. 104:201-231, 2004
dc.identifierdoi:10.1023/B:GEOM.0000022861.52942.98
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99790
dc.subjectDifferential Geometry
dc.subject53C17, 53C42, 49Q10
dc.titleMinimal surfaces in the Heisenberg group
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