Abstract
We give an example of a \(\mathcal{C}^{3-\epsilon}\)-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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Bonk, M., Heinonen, J. Smooth quasiregular mappings with branching. Publ. Math., Inst. Hautes Étud. Sci. 100, 153–170 (2004). https://doi.org/10.1007/s10240-004-0024-8
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DOI: https://doi.org/10.1007/s10240-004-0024-8