Convex functions on Carnot groups

  • Petri Juutinen

    University of Jyväskylä, Finland
  • Guozhen Lu

    Wayne State University, Detroit, USA
  • Juan J. Manfredi

    University of Pittsburgh, United States
  • Bianca Stroffolini

    Università degli Studi di Napoli Federico II, Italy


We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.

Cite this article

Petri Juutinen, Guozhen Lu, Juan J. Manfredi, Bianca Stroffolini, Convex functions on Carnot groups. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 191–200

DOI 10.4171/RMI/490