Calculus of Variations and Geometric Measure Theory
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V. Barone Adesi - F. Serra Cassano - D. Vittone

The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

created by vittone on 08 Mar 2006
modified on 05 Oct 2007


Published Paper

Inserted: 8 mar 2006
Last Updated: 5 oct 2007

Journal: Calc. Var. & PDEs
Volume: 30
Number: 1
Pages: 17-49
Year: 2007


In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Carathéodory (CC) structures. More precisely we will introduce a general {\it calibration method} in this setting and we will study the {\it 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 $n\geq 5$.

Keywords: minimal surfaces, Carnot-Carathéodory spaces, Heisenberg group, calibrations, Bernstein problem


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