Properties of close-to-harmonic mappings
type: Item
instance of: scholarly article
title: Properties of close-to-harmonic mappings
zbMATH Open document ID: 0966.58008
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: Let \(U\) be an open subset of \(\mathbb{R}^n\). The paper is concerned with continuously differentiable mappings \(f: U\to \mathbb{R}^m\) that satisfy certain Sobolev-type conditions and are close (in terms of local deviation in the \(C^1\)-norm) to harmonic mappings. A large number of theorems are announced, but no proofs are given. Among the announced results are analogues of the classical Liouville theorem for bounded harmonic functions on \(\mathbb{R}^n\) and theorems about the topological properties of certain classes of close-to-harmonic mappings. The paper is related to, and to a certain extent depends upon, an earlier paper of the author [see Zbl 0958.58013].
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 1557579
zbMATH Keywords: harmonic mappings
zbMATH Keywords: Liouville theorem for bounded harmonic functions
zbMATH Keywords: close-to-harmonic mappings
author: Anatoliĭ Pavlovich Kopylov
reviewed by: D. H. Armitage
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557579