CONVEXITY AND HORIZONTAL SECOND FUNDAMENTAL FORMS FOR HYPERSURFACES IN CARNOT GROUPS

被引：12

作者：

Capogna, Luca ^{[1
]}

Pauls, Scott D. ^{[2
]}

Tyson, Jeremy T. ^{[3
]}

机构：

[1] Univ Arkansas, Dept Math, Fayetteville, AR 72701 USA

[2] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 362卷 / 08期

基金：

美国国家科学基金会;

关键词：

Convexity; Carnot group; second fundamental form; Riemannian approximation; HEISENBERG-GROUP; MEAN-CURVATURE; SURFACES; THEOREM; SPACES; FLOW;

D O I：

10.1090/S0002-9947-10-04768-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：4045 / 4062

页数：18

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