The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

  • Vittorio Barone Adesi
  • Francesco Serra Cassano
  • Davide Vittone
Original Article

DOI: 10.1007/s00526-006-0076-3

Cite this article as:
Adesi, V.B., Cassano, F.S. & Vittone, D. Calc. Var. (2007) 30: 17. doi:10.1007/s00526-006-0076-3

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 a meaningful and simpler class of CC spaces, i.e. the Heisenberg group \({\mathbb{H}^n}\) . In particular we will positively answer to the Bernstein problem in the case n =  1 and we will provide counter examples when \({n\geq 5}\) .

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Vittorio Barone Adesi
    • 1
  • Francesco Serra Cassano
    • 1
  • Davide Vittone
    • 2
  1. 1.Dipartimento di MatematicaUniversità di TrentoPovo (Trento)Italy
  2. 2.Scuola Normale SuperiorePisaItaly