Convexity and horizontal second fundamental forms for hypersurfaces in carnot groups

Luca Capogna, Scott D. Pauls, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

We use a Riemannian approximation scheme to give a characterization for smooth convex functions on a Carnot group (in the sense of Danielli-Garofalo- Nhieu or Lu-Manfredi-Stroffolini) in terms of the positive semidefiniteness of the horizontal second fundamental form of their graph.

Original languageEnglish (US)
Pages (from-to)4045-4062
Number of pages18
JournalTransactions of the American Mathematical Society
Volume362
Issue number8
DOIs
StatePublished - Aug 2010

Keywords

  • Carnot group
  • Convexity
  • Riemannian approximation
  • Second fundamental form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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