Publications Mathématiques de l'Institut des Hautes Études Scientifiques

, Volume 100, Issue 1, pp 153-170

First online:

Smooth quasiregular mappings with branching

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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.