Displaying similar documents to “Liouville type theorems for mappings with bounded (co)-distortion”

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.

Squeezing the Sierpinski sponge

Tadeusz Iwaniec, Gaven Martin (2002)

Studia Mathematica

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We give an example relating to the regularity properties of mappings with finite distortion. This example suggests conditions to be imposed on the distortion function in order to avoid "cavitation in measure".