Convex functions on Carnot groups
Petri Juutinen
University of Jyväskylä, FinlandGuozhen Lu
Wayne State University, Detroit, USAJuan J. Manfredi
University of Pittsburgh, United StatesBianca Stroffolini
Università degli Studi di Napoli Federico II, Italy
Abstract
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