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

According to a theorem of Martio, Rickman and Väisälä, all nonconstant C n/(n-2) -smooth quasiregular maps in 𝐑 n , n3, 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 n5 we construct a C 1+ϵ(n) -smooth quasiregular map in 𝐑 n with nonempty branch set.

@article{PMIHES_2005__101__209_0,
     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},
     publisher = {Springer},
     volume = {101},
     year = {2005},
     pages = {209-241},
     doi = {10.1007/s10240-005-0031-4},
     zbl = {1078.30015},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2005__101__209_0}
}
Kaufman, Robert; Tyson, Jeremy T.; Wu, Jang-Mei. Smooth quasiregular maps with branching in $\mathbf {R}^n$. Publications Mathématiques de l'IHÉS, Volume 101 (2005) , pp. 209-241. doi : 10.1007/s10240-005-0031-4. http://www.numdam.org/item/PMIHES_2005__101__209_0/

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