The Bernstein Problem in the Heisenberg Group

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.

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

Cited by in corpus (2)

• Constant mean curvature surfaces in sub-Riemannian geometry
• H-minimal graphs of low regularity in the Heisenberg group