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The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

V. Barone Adesi·F. Serra Cassano·D. Vittone
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Abstract

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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V. Barone Adesi, F. Serra Cassano, D. Vittone. 2006-08-03. The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations. https://arxiv.org/abs/math/0608092

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