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Revista Matemática Iberoamericana

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Volume 23, Issue 1, 2007, pp. 191–200
DOI: 10.4171/RMI/490

Published online: 2007-04-30

Convex functions on Carnot groups

Petri Juutinen[1], Guozhen Lu[2], Juan J. Manfredi[3] and Bianca Stroffolini[4]

(1) University of Jyväskylä, Finland
(2) Wayne State University, Detroit, USA
(3) University of Pittsburgh, United States
(4) 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.

Keywords: Horizontal convexity, viscosity convexity, Carnot groups, subelliptic equations

Juutinen Petri, Lu Guozhen, Manfredi Juan, Stroffolini Bianca: Convex functions on Carnot groups. Rev. Mat. Iberoam. 23 (2007), 191-200. doi: 10.4171/RMI/490