Graphs of Lipschitz functions and minimal surfaces on Carnot groups
type: Item
instance of: scholarly article
title: Graphs of Lipschitz functions and minimal surfaces on Carnot groups
zbMATH Open document ID: 1257.53050
DOI: 10.1134/S1064562412040199
author: M. Karmanova
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: The author proves an area formula for the graphs of a class of Lipschitz mappings defined on Carnot groups. The main tool is the introduction of a new intrinsic structure adapted to the mapping under consideration and certain polynomial sub-Riemannian differentiability. As an application, the author obtains an analytical description of surfaces minimal with respect to the intrinsic measure.
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 6106499
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Carnot groups
zbMATH Keywords: Lipschitz functions
reviewed by: Miroslav Doupovec
MaRDI profile type: Publication
cites work: Q5459459
cites work: Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group \(\mathbb H^1\)
cites work: A coarea formula for smooth contact mappings of Carnot manifolds
cites work: Q3729194
cites work: Stratified Lie Groups and Potential Theory for their Sub-Laplacians
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
cites work: An area formula for Lipschitz mappings of Carnot-Carathéodory spaces
description: scientific article; zbMATH DE number 6106499