On convergence theorems for space quasiregular mappings

: Gutlyanskiǐ V., Martio O., Ryazanov V., Vuorinen M.

: 1998

Forum Mathematicum

: Forum Mathematicum

: 10

: 3

: 353

: 375

: 23

: 0933-7741

: http://api.elsevier.com/content/abstract/scopus_id:0032222310

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).