Smooth quasiregular maps with branching in ${𝐑}^n$

Kaufman, Robert ; Tyson, Jeremy T. ; Wu, Jang-Mei

Publications Mathématiques de l'IHÉS, Tome 101 (2005), pp. 209-241.

Résumé

According to a theorem of Martio, Rickman and Väisälä, all nonconstant $C^{n/(n-2)}$-smooth quasiregular maps in ${𝐑}^n$, $n\ge 3$, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in ${𝐑}^3$. We prove that the order of smoothness is sharp in ${𝐑}^4$. For each $n\ge 5$ we construct a $C^{1+ϵ\left(n\right)}$-smooth quasiregular map in ${𝐑}^n$ with nonempty branch set.

Détail

DOI : 10.1007/s10240-005-0031-4

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