A capacity estimate on Carnot groups
type: Item
instance of: scholarly article
title: A capacity estimate on Carnot groups
zbMATH Open document ID: 0842.22007
author: Juha Heinonen
published in: Bulletin des Sciences Mathématiques
publication date: 1996-08-04T00:00:00Z
review text: The capacity \(\text{cap}_Q(F_1, F_2, N)\) of any condenser \((F_1, F_2, N)\) (where \(N\) is a connected, simply connected compact stratified nilpotent Lie group, \(Q\) is the homogeneous dimension of \(N\), and \(F_1\) and \(F_2\) are closed subsets of \(N\) which satisfy some rather particular conditions) is shown to be bounded from below by a universal positive constant \(\delta\), depending on \(N\) only. Also, some relations between capacities of the form \(\text{cap}_p (\partial U, F, U)\), where \(U\) is an open subset of \(N\), and the Hausdorff dimension of \(F\) are established.
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 833465
zbMATH Keywords: capacity
zbMATH Keywords: condenser
zbMATH Keywords: nilpotent Lie group
zbMATH Keywords: Hausdorff dimension
reviewed by: Paweł Walczak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 833465