Mappings of finite distortion: Global homeomorphism theorem.

Holopainen, Ilkka; Pankka, Pekka

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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.