Polar coordinates in Carnot groups
type: Item
instance of: scholarly article
title: Polar coordinates in Carnot groups
zbMATH Open document ID: 1015.22005
author: Zoltán M. Balogh
author: Jeremy T. Tyson
published in: Mathematische Zeitschrift
publication date: 2003-06-02T00:00:00Z
review text: In the present paper, the authors describe a procedure for constructing ``polar coordinates'' in a certain class of Carnot groups. They show that the given construction can be carried out in groups of Heisenberg type and they give explicit formulas for the polar coordinate decomposition in that setting. The construction makes use of nonlinear potential theory, specifically, fundamental solutions for the \(p-\)Laplace operators. As applications of this result, the authors obtain exact capacity estimates, representation formulas and an explicit sharp constant for the Moser-Trudinger inequality. Topological and measure-theoretic consequences for quasiregular mappings are also obtained.
reviewed by: Neculai Papaghiuc
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1922564
zbMATH Keywords: Polar coordinates
zbMATH Keywords: Carnot groups
zbMATH Keywords: Moser-Trudinger inequality
zbMATH Keywords: quasiregular mappings
MaRDI profile type: Publication
full work available at URL: s00209-002-0441-7
OpenAlex ID: W2057848911
DOI: 10.1007/S00209-002-0441-7
description: scientific article; zbMATH DE number 1922564