Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group
Differential Geometry
2007-05-23 v1 Analysis of PDEs
Abstract
Let S be a C^2 H-minimal noncharacteristic hypersurface in the first Heisenberg group. We show that if S contains a graphical strip, then it is not a stable minimal surface. Moreover, we show that if S is a C^2 H-minimal noncharacteristic entire graph which is not itself a vertical plane, then S contains a graphical strip. Thus, as a corollary, we obtain an analogue of the Bernstein theorem: the only stable C^2 H-minimal noncharacteristic entire graphs are the vertical planes.
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Cite
@article{arxiv.math/0608516,
title = {Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group},
author = {D. Danielli and N. Garofalo and D. M. Nhieu and S. D. Pauls},
journal= {arXiv preprint arXiv:math/0608516},
year = {2007}
}
Comments
33 pages