Smooth quasiregular mappings with branching
Publications Mathématiques de l'IHÉS, Tome 100 (2004), pp. 153-170.

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 n-space has Hausdorff dimension quantitatively bounded away from n. By using the second result, we establish a new, qualitatively sharp relation between smoothness and branching.

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     author = {Bonk, Mario and Heinonen, Juha},
     title = {Smooth quasiregular mappings with branching},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {153--170},
     publisher = {Springer},
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     year = {2004},
     doi = {10.1007/s10240-004-0024-8},
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     url = {http://archive.numdam.org/articles/10.1007/s10240-004-0024-8/}
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Bonk, Mario; Heinonen, Juha. Smooth quasiregular mappings with branching. Publications Mathématiques de l'IHÉS, Tome 100 (2004), pp. 153-170. doi : 10.1007/s10240-004-0024-8. http://archive.numdam.org/articles/10.1007/s10240-004-0024-8/

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