Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs

被引：22

作者：

Bigolin, Francesco ^{[1
]}

Cassano, Francesco Serra ^{[1
]}

机构：

[1] Univ Trent, Dipartimento Matemat, I-38050 Trento, Italy

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2010年 / 3卷 / 01期

关键词：

Heisenberg group; Carnot-Caratheodory metric; intrinsic graph; non-linear first-order PDEs; CARNOT-CARATHEODORY SPACES; IMPLICIT FUNCTION THEOREM; BERNSTEIN PROBLEM; RECTIFIABILITY; SUBMANIFOLDS; HYPERSURFACES; PERIMETER;

D O I：

10.1515/ACV.2010.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We continue to study H-regular graphs, a class of intrinsic regular hypersurfaces in the Heisenberg group H-n = C-n x R R2n+1 endowed with a left-invariant metric d(infinity) equivalent to its Carnot-Caratheodory metric. Here we investigate their relationships with suitable weak solutions of non-linear first-order PDEs. As a consequence this implies some of their geometric properties: a uniqueness result for H-regular graphs of prescribed horizontal normal as well as their (Euclidean) regularity as long as there is regularity on the horizontal normal.

引用

页码：69 / 97

页数：29

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