Stable complete embedded minimal surfaces in $\mathbb H^1$ with empty characteristic locus are vertical planes
Differential Geometry
2009-03-26 v1
Abstract
In the recent paper \cite{DGNP} we have proved that the only stable minimal surfaces in the first Heisenberg group 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 complete embedded minimal surfaces in with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane.
Cite
@article{arxiv.0903.4296,
title = {Stable complete embedded minimal surfaces in $\mathbb H^1$ with empty characteristic locus are vertical planes},
author = {Donatella Danielli and Nicola Garofalo and Duy-Minh Nhieu and Scott Pauls},
journal= {arXiv preprint arXiv:0903.4296},
year = {2009}
}