Convexity and Horizontal Second Fundamental Forms for Hypersurfaces in Carnot Groups

Authors

Luca Capogna, University of ArkansasFollow
Scott D. Pauls, Dartmouth College
Jeremy T. Tyson, University of Illinois Urbana-Champaign

Document Type

Article

Publication Date

8-1-2010

Publication Title

Transactions of the American Mathematical Society

Abstract

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.

Keywords

Carnot group, Convexity, Riemannian approximation, Second fundamental form

Volume

362

Issue

8

First Page

4045

Last Page

4062

DOI

10.1090/S0002-9947-10-04768-9

ISSN

00029947

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Capogna, Luca; Pauls, Scott D.; and Tyson, Jeremy T., "Convexity and Horizontal Second Fundamental Forms for Hypersurfaces in Carnot Groups" (2010). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/138