We give an example of a -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.
@article{PMIHES_2004__100__153_0,
author = {Bonk, Mario and Heinonen, Juha},
title = {Smooth quasiregular mappings with branching},
journal = {Publications Math\'ematiques de l'IH\'ES},
volume = {99},
year = {2004},
pages = {153-170},
doi = {10.1007/s10240-004-0024-8},
mrnumber = {2102699},
zbl = {1063.30021},
language = {en},
url = {http://dml.mathdoc.fr/item/PMIHES_2004__100__153_0}
}
Bonk, Mario; Heinonen, Juha. Smooth quasiregular mappings with branching. Publications Mathématiques de l'IHÉS, Tome 99 (2004) pp. 153-170. doi : 10.1007/s10240-004-0024-8. http://gdmltest.u-ga.fr/item/PMIHES_2004__100__153_0/
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