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On local injectivity and asymptotic linearity of quasiregular mappings

V. Gutlyanskiĭ; O. Martio; V. Ryazanov; M. Vuorinen — 1998

Studia Mathematica

It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at $x_{0}$ implies the local injectivity and the asymptotic linearity of f at $x_{0}$ . Sufficient conditions for $l o g | f (x) - f (x_{0}) |$ to behave asymptotically as $l o g | x - x_{0} |$ are given. Some global injectivity results are derived.