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Displaying similar documents to “On local injectivity and asymptotic linearity of quasiregular mappings”

Smooth quasiregular mappings with branching

Mario Bonk, Juha Heinonen (2004)

Publications Mathématiques de l'IHÉS

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We give an example of a 𝒞 3 - ϵ -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in-space has Hausdorff dimension quantitatively bounded away from . By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.