Smooth quasiregular maps with branching in 𝐑 n
Publications Mathématiques de l'IHÉS, Tome 101 (2005), pp. 209-241.

According to a theorem of Martio, Rickman and Väisälä, all nonconstant C n/(n-2) -smooth quasiregular maps in 𝐑 n , n≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in 𝐑 3 . We prove that the order of smoothness is sharp in 𝐑 4 . For each n≥5 we construct a C 1+ϵ(n) -smooth quasiregular map in 𝐑 n with nonempty branch set.

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     author = {Kaufman, Robert and Tyson, Jeremy T. and Wu, Jang-Mei},
     title = {Smooth quasiregular maps with branching in $\mathbf {R}^n$},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {209--241},
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     url = {http://archive.numdam.org/articles/10.1007/s10240-005-0031-4/}
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Kaufman, Robert; Tyson, Jeremy T.; Wu, Jang-Mei. Smooth quasiregular maps with branching in $\mathbf {R}^n$. Publications Mathématiques de l'IHÉS, Tome 101 (2005), pp. 209-241. doi : 10.1007/s10240-005-0031-4. http://archive.numdam.org/articles/10.1007/s10240-005-0031-4/

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