We consider the definition and regularity properties of convexfunctions in Carnot groups. We show that various notions ofconvexity in the subelliptic setting that have appeared in theliterature are equivalent. Our point of view is based on thinkingof convex functions as subsolutions of homogeneous ellipticequations.
"Convex functions on Carnot groups." Rev. Mat. Iberoamericana 23 (1) 191 - 200, April, 2007.