Minimal graph-surfaces on arbitrary two-step Carnot groups

被引：2

作者：

Karmanova, M. B. ^{[1
]}

机构：

[1] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, 4 Acad Koptyug Ave, Novosibirsk 630090, Russia

来源：

RUSSIAN MATHEMATICS | 2019年 / 63卷 / 05期

关键词：

two-step Carnot group; graph-mapping; minimal surface; mean curvature; CARATHEODORY SPACES; DIFFERENTIABILITY; GEOMETRY;

D O I：

10.3103/S1066369X19050025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish basic properties of minimal graph-surfaces constructed from classes of mappings defined on two-step Carnot groups. The research methods include solving the question, specific for the case under study, on correctness of the problem statement. The main result on necessary minimality conditions is formulated in terms of a sub-Riemannian analog of mean curvature.

引用

页码：13 / 26

页数：14

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