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arXiv · 0903.4296

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

Donatella Danielli·Nicola Garofalo·Duy-Minh Nhieu·Scott Pauls
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Abstract

In 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.

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Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott Pauls. 2009-03-25. Stable complete embedded minimal surfaces in $\mathbb H^1$ with empty characteristic locus are vertical planes. https://arxiv.org/abs/0903.4296

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