Infinitesimal geometry of quasilinear mappings.

Gutlyanskij, V.Ya.; Martio, O.; Ryazanov, V.I.; Vuorinen, M.

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Mappings of finite distortion: Removability of Cantor sets.

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According to a theorem of Martio, Rickman and Väisälä, all nonconstant C-smooth quasiregular maps in , ≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in . We prove that the order of smoothness is sharp in . For each ≥5 we construct a C-smooth quasiregular map in with nonempty branch set.

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Rickman, Seppo (1995)

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On local injectivity and asymptotic linearity of quasiregular mappings

V. Gutlyanskiĭ, O. Martio, V. Ryazanov, M. Vuorinen (1998)

Studia Mathematica

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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.