Integrability of the sub-riemannian mean curvature of surfaces in the heisenberg group

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The problem of the local summability of the sub-Riemannian mean curvature H of a hypersurface M in the Heisenberg group, or in more general Carnot groups, near the characteristic set of M arises naturally in several questions in geometric measure theory. We construct an example which shows that the sub-Riemannian mean curvature H of a C2 surface M in the Heisenberg group H1 in general fails to be integrable with respect to the Riemannian volume on M.

Original languageEnglish (US)
Pages (from-to)811-821
Number of pages11
JournalProceedings of the American Mathematical Society
Volume140
Issue number3
DOIs
StatePublished - 2012
Externally publishedYes

Keywords

  • First and second variation
  • H-mean curvature
  • Integration by parts
  • Minimal surfaces
  • Monotonicity of the H-perimeter

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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