The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

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In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Caratheodory (CC) structures. More precisely we will introduce a general calibration method in this setting and we will study the Bernstein problem for entire regular intrinsic minimal graphs in a meaningful and simpler class of CC spaces, i.e. the Heisenberg group H^n. In particular we will positively answer to the Bernstein problem in the case n=1 and we will provide counterexamples when n>=5.

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Classical Analysis and ODEs, Metric Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/115276

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608092
 http://arxiv.org/abs/math/0608092

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arXiv