Equivalence of the Apollonian and its inner metric.
Hästö, Peter, Ponnusamy, S., Sahoo, S.K. (2010)
International Journal of Mathematics and Mathematical Sciences
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Hästö, Peter, Ponnusamy, S., Sahoo, S.K. (2010)
International Journal of Mathematics and Mathematical Sciences
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According to a theorem of Martio, Rickman and Väisälä, all nonconstant C-smooth quasiregular maps in , ≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in . We prove that the order of smoothness is sharp in . For each ≥5 we construct a C-smooth quasiregular map in with nonempty branch set.
Cristea, M. (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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International Journal of Mathematics and Mathematical Sciences
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