Transactions of the American Mathematical Society
We use a Riemannian approximation scheme to give a characterization for smooth convex functions on a Carnot group (in the sense of Danielli-Garofalo- Nhieu or Lu-Manfredi-Stroffolini) in terms of the positive semidefiniteness of the horizontal second fundamental form of their graph.
Carnot group, Convexity, Riemannian approximation, Second fundamental form
Capogna, Luca; Pauls, Scott D.; and Tyson, Jeremy T., "Convexity and Horizontal Second Fundamental Forms for Hypersurfaces in Carnot Groups" (2010). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.