%0 Journal Article
%T Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group
%A D. Danielli
%A N. Garofalo
%A D. M. Nhieu
%A S. D. Pauls
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0608516v1