Calculus of Variations and Geometric Measure Theory

P. Juutinen - G. Lu - J. Manfredi - B. Stroffolini

"Convex functions on Carnot groups "

created by stroffoli on 09 Nov 2005


Accepted Paper

Inserted: 9 nov 2005

Journal: Revista Matematica Iberoamericana
Year: 2005


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: Carnot groups, horizontal convexity, viscosity convexity, subelliptic equations