The Phragmen-Lindelöf principle for quasiregular mappings of manifolds and the isoperimetry
type: Item
instance of: scholarly article
title: The Phragmen-Lindelöf principle for quasiregular mappings of manifolds and the isoperimetry
zbMATH Open document ID: 0886.30020
author: O. Martio
author: M. Vuorinen
author: V. M. Miklyukov
published in: Doklady Mathematics
publication date: 1998-05-06T00:00:00Z
review text: The authors consider quasiregular mappings of a noncompact Riemannian manifold \(D\) in view of generalizations of the Phragmén-Lindelöf principle. Roughly speaking, the main result may be expressed as follows. Either the quasiregular mapping \(f\) grows rapidly in a certain sense or \(f\equiv\text{const}\) (Theorem 2). Finally, the authors give two applications of Theorem 2 to a quasiregular mapping \(f=(f_1,f_2, \dots, f_n): \mathbb{R}^n \supset D\to \mathbb{R}^n\) with \(f_1\leq 1\) on the boundary of \(D\), where \(D\) is a cone or a semicylinder, respectively. In this paper, the proofs are based on isoperimetry. This new approach allows the consideration of the Phragmén-Lindelöf principle for quasiregular mappings of manifolds.
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 1113092
zbMATH Keywords: quasiregular mappings
zbMATH Keywords: Phragmen-Lindelöf principle
reviewed by: Erich Hoy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1113092