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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Convexity And Horizontal Second Fundamental Forms For Hypersurfaces In Carnot Groups, Luca Capogna, Scott D. Pauls, Jeremy T. Tyson
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.
A Note On The Engulfing Property And The R 1+Α -Regularity Of Convex Functions In Carnot Groups, Luca Capogna, Diego Maldonado
A Note On The Engulfing Property And The R 1+Α -Regularity Of Convex Functions In Carnot Groups, Luca Capogna, Diego Maldonado
Mathematics Sciences: Faculty Publications
We study the engulfing property for convex functions in Carnot groups. As an application we show that the horizontal gradient of functions with this property is Hölder continuous.