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On convergence theorems for space quasiregular mappings
Tekijät: Gutlyanskiǐ V., Martio O., Ryazanov V., Vuorinen M.
Julkaisuvuosi: 1998
Lehti:: Forum Mathematicum
Tietokannassa oleva lehden nimi: Forum Mathematicum
Vuosikerta: 10
Numero: 3
Aloitussivu: 353
Lopetussivu: 375
Sivujen määrä: 23
ISSN: 0933-7741
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:0032222310
Tiivistelmä
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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