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Convexity And Horizontal Second Fundamental Forms For Hypersurfaces In Carnot Groups, Luca Capogna, Scott D. Pauls, Jeremy T. Tyson

Mathematics Sciences: Faculty Publications

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.