A notable family of entire intrinsic minimal graphs in the heisenberg group which are not perimeter minimizing

D. Danielli, N. Garofalo, D. M. Nhieu

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

One of the main objectives of this paper is to unravel a new interesting phenomenon of the sub-Riemannian Bernstein problem with respect to its Euclidean ancestor, with the purpose of also indicating a possible line of attack toward its solution. We show that the global intrinsic graphs (1.2) are unstable critical points of the horizontal perimeter. As a consequence of this fact, the study of the stability acquires a central position in the problem itself.

Original languageEnglish (US)
Pages (from-to)317-339
Number of pages23
JournalAmerican Journal of Mathematics
Volume130
Issue number2
DOIs
StatePublished - Apr 2008
Externally publishedYes

Keywords

  • First and second variation formulas
  • H-minimal surfaces
  • Intrinsic graphs

ASJC Scopus subject areas

  • Mathematics(all)

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