Analogues of Sokhotski-Weierstrass and Picard theorems for mappings with finite length distortion
type: Item
instance of: scholarly article
zbMATH Open document ID: 1249.30074
publication date: 2012-07-31T00:00:00Z
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 30C75
zbMATH DE Number: 6062150
zbMATH Keywords: Sokhotski-Weierstrass theorems
zbMATH Keywords: mappings with finite length distortion
zbMATH Keywords: isolated singularities
zbMATH Keywords: Picard theorems
author: Evgeny Sevost'yanov
MaRDI profile type: Publication
title: Analogues of Sokhotski-Weierstrass and Picard theorems for mappings with finite length distortion
published in: Trudy Instituta Prikladnoĭ Matematiki i Mekhaniki
review text: The present article is devoted to the study of mappings with finite length distortion introduced by O. Martio, V. Ryazanov, U. Srebro and E. Yakubov in 2004. It is proved that isolated singularities are removable for open discrete mappings with finite length distortion provided that the inner dilatation has finite mean oscillation or logarithmic singularities of the order at most \(n-1\) on the corresponding set. As applications, analogues of the well-known Sokhotski-Weierstrass and Picard theorems are proved. In particular, it is shown that the mappings take any value in arbitrarily small neighborhoods of the essential singularity except, possibly, a set of capacity zero. The results of the work can be applied to various classes of spatial mappings with finite distortion.
reviewed by: Vladimir I. Ryazanov
description: scientific article; zbMATH DE number 6062150