CONVEXITY AND HORIZONTAL SECOND FUNDAMENTAL FORMS FOR HYPERSURFACES IN CARNOT GROUPS

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.

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2010-08, Vol.362 (8), p.4045-4062
Main Authors: CAPOGNA, LUCA, PAULS, SCOTT D., TYSON, JEREMY T.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Approximation
Convexity
Coordinate systems
Curvature
Exact sciences and technology
General mathematics
General, history and biography
Hypersurfaces
Mathematical functions
Mathematical theorems
Mathematics
Sciences and techniques of general use
Symmetry
Vector fields
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Summary: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-10-04768-9