The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
Classical Analysis and ODEs
2007-05-23 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/0608092,
title = {The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations},
author = {V. Barone Adesi and F. Serra Cassano and D. Vittone},
journal= {arXiv preprint arXiv:math/0608092},
year = {2007}
}