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

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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.
33 pages

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Differential Geometry, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/115500

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608516
 http://arxiv.org/abs/math/0608516

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arXiv