The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

Details The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

2006-08-03

arxiv.org/abs/math/0608092v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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