Publications mathématiques de l'IHÉS

, Volume 100, Issue 1, pp 153–170

Smooth quasiregular mappings with branching

Article

DOI: 10.1007/s10240-004-0024-8

Cite this article as:
Bonk, M. & Heinonen, J. Publ. Math., Inst. Hautes Étud. Sci. (2004) 100: 153. doi:10.1007/s10240-004-0024-8

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.

Copyright information

© Institut des Hautes Études Scientifiques and Springer-Verlag 2004

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

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