Closed polar sets in a Riemannian manifold
type: Item
instance of: scholarly article
title: Closed polar sets in a Riemannian manifold
zbMATH Open document ID: 1191.31005
author: Victor Anandam
author: Suad AlHemedan
published in: Arab Journal of Mathematical Sciences
publication date: 2010-01-13T00:00:00Z
review text: This paper is concerned with a characterization of polar sets in Riemann manifolds. More precisely, the authors establish that a subset \(E\) of a parabolic Riemannian manifold \(R\) is polar if and only if there exists a harmonic function \(u\) on \(R\setminus E\) whose limit at any point of \(\partial(R\setminus E)\) is infinity. In case the Riemannian manifold is of hyperbolic type, the above characterization is also equivalent to the existence of a positive harmonic function \(u\) having the above property.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 31C12
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 5657225
zbMATH Keywords: Harmonic extensions
zbMATH Keywords: polar sets
zbMATH Keywords: Riemannian manifold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5657225