Convexity and horizontal second fundamental forms for hypersurfaces in carnot groups

Luca Capogna; Scott D. Pauls; Jeremy T. Tyson

doi:10.1090/S0002-9947-10-04768-9

Convexity and horizontal second fundamental forms for hypersurfaces in carnot groups

Luca Capogna, Scott D. Pauls, Jeremy T. Tyson

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	4045-4062
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9947-10-04768-9
State	Published - Aug 2010

Keywords

Carnot group
Convexity
Riemannian approximation
Second fundamental form

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Online availability

10.1090/S0002-9947-10-04768-9

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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.",

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AU - Pauls, Scott D.

AU - Tyson, Jeremy T.

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KW - Carnot group

KW - Convexity

KW - Riemannian approximation

KW - Second fundamental form

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Convexity and horizontal second fundamental forms for hypersurfaces in carnot groups

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

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