Stable complete embedded minimal surfaces in $\mathbb H^1$ with empty characteristic locus are vertical planes

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dc.creatorDanielli, Donatella
dc.creatorGarofalo, Nicola
dc.creatorNhieu, Duy-Minh
dc.creatorPauls, Scott
dc.date2009-03-25
dc.date.accessioned2026-07-07T12:56:26Z
dc.date.available2026-07-07T12:56:26Z
dc.descriptionIn the recent paper \cite{DGNP} we have proved that the only stable $C^2$ minimal surfaces in the first Heisenberg group $\Hn$ which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in \cite{DGNP} to $C^2$ complete embedded minimal surfaces in $\mathbb H^1$ with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane.
dc.identifierhttps://arxiv.org/abs/0903.4296
dc.identifierhttp://arxiv.org/abs/0903.4296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224580
dc.subjectDifferential Geometry
dc.titleStable complete embedded minimal surfaces in $\mathbb H^1$ with empty characteristic locus are vertical planes
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