In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Carathéodory (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 ameaningful 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 counter examples when n ≥ 5.
The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
VITTONE, DAVIDE
2007
Abstract
In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Carathéodory (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 ameaningful 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 counter examples when n ≥ 5.
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