Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group

Details Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group

2006-08-21

arxiv.org/abs/math/0608516v1

Mathematics

Differential Geometry

33 pages

Scientific paper

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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