According to a theorem of Martio, Rickman and Väisälä, all nonconstant C n/(n-2)-smooth quasiregular maps in Rn, n≥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≥5 we construct a C 1+ε(n)-smooth quasiregular map in R n with nonempty branch set.
|Original language||English (US)|
|Number of pages||33|
|Journal||Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques|
|State||Published - Jun 2005|
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