Isoperimetric inequalities and Dirichlet functions of Riemann surfaces
type: Item
instance of: scholarly article
title: Isoperimetric inequalities and Dirichlet functions of Riemann surfaces
zbMATH Open document ID: 0813.30034
DOI: 10.5565/PUBLMAT_38194_19
author: José M. Rodríguez
published in: Publicacions Matemàtiques
publication date: 1995-05-17T00:00:00Z
review text: Let \(\mathcal S\) be a complete Riemann surface with a metric of constant curvature \(-1\). The author shows that if \(\mathcal S\) has a linear isoperimetric inequality and also satisfies an extra condition of regularity, then there exists a non-constant harmonic function \(h\) with finite Dirichlet integral over \(\mathcal S\). The author gives an example of a surface \(\mathcal S\) where this regularity condition fails and where such an \(h\) does not exist.
Mathematics Subject Classification ID: 30F15
zbMATH DE Number: 722048
reviewed by: Peter B. Gilkey
MaRDI profile type: Publication
full work available at URL: publmat 38194 19
OpenAlex ID: W2054996260
description: scientific article; zbMATH DE number 722048