The Bernstein Problem in the Heisenberg Group
Differential Geometry
2007-05-23 v2 Analysis of PDEs
Abstract
We establish the following theorem of Bernstein type for the first Heisenberg group: Let S be a C^2 connected H-minimal surface which is a graph over some plane P, then S is either a non-characteristic vertical plane, or its generalized seed curve satisfies a type of constant curvature condition.
Cite
@article{arxiv.math/0209065,
title = {The Bernstein Problem in the Heisenberg Group},
author = {Nicola Garofalo and Scott D. Pauls},
journal= {arXiv preprint arXiv:math/0209065},
year = {2007}
}
Comments
62 pages, 9 figures. The first version of this paper contained a serious error. The current version is a complete reworking of the techniques and results