A1 Refereed original research article in a scientific journal
On convergence theorems for space quasiregular mappings
Authors: Gutlyanskiǐ V., Martio O., Ryazanov V., Vuorinen M.
Publication year: 1998
Journal:: Forum Mathematicum
Journal name in source: Forum Mathematicum
Volume: 10
Issue: 3
First page : 353
Last page: 375
Number of pages: 23
ISSN: 0933-7741
Web address : http://api.elsevier.com/content/abstract/scopus_id:0032222310
Abstract
Convergence problems are studied for quasiregular mappings in space. We show the continuity of the injectivity radius for arbitrary continuous discrete sense-preserving mappings and prove a space version of the Strebel convergence theorem for the local dilatation. We give the Bers-Bojarski convergence theorem in terms of the matrix dilatation. We establish a sharp upper semicontinuity result for distortion coefficients in the mean. These theorems are used to give some extensions of Liouville's theorem (Lavrentiev-Reshetnyak).
Convergence problems are studied for quasiregular mappings in space. We show the continuity of the injectivity radius for arbitrary continuous discrete sense-preserving mappings and prove a space version of the Strebel convergence theorem for the local dilatation. We give the Bers-Bojarski convergence theorem in terms of the matrix dilatation. We establish a sharp upper semicontinuity result for distortion coefficients in the mean. These theorems are used to give some extensions of Liouville's theorem (Lavrentiev-Reshetnyak).
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