Smooth quasiregular maps with branching in 𝐑 n

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

Publications Mathématiques de l'IHÉS (2005)

  • Volume: 101, page 209-241
  • ISSN: 0073-8301

Abstract

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According to a theorem of Martio, Rickman and Väisälä, all nonconstant Cn/(n-2)-smooth quasiregular maps in Rn, n≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in R3. We prove that the order of smoothness is sharp in R4. For each n≥5 we construct a C1+ε(n)-smooth quasiregular map in Rn with nonempty branch set.

How to cite

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Kaufman, Robert, Tyson, Jeremy T., and Wu, Jang-Mei. "Smooth quasiregular maps with branching in $\mathbf {R}^n$." Publications Mathématiques de l'IHÉS 101 (2005): 209-241. <http://eudml.org/doc/104210>.

@article{Kaufman2005,
abstract = {According to a theorem of Martio, Rickman and Väisälä, all nonconstant Cn/(n-2)-smooth quasiregular maps in Rn, n≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in R3. We prove that the order of smoothness is sharp in R4. For each n≥5 we construct a C1+ε(n)-smooth quasiregular map in Rn with nonempty branch set.},
author = {Kaufman, Robert, Tyson, Jeremy T., Wu, Jang-Mei},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {space quasiregular mappings},
language = {eng},
pages = {209-241},
publisher = {Springer},
title = {Smooth quasiregular maps with branching in $\mathbf \{R\}^n$},
url = {http://eudml.org/doc/104210},
volume = {101},
year = {2005},
}

TY - JOUR
AU - Kaufman, Robert
AU - Tyson, Jeremy T.
AU - Wu, Jang-Mei
TI - Smooth quasiregular maps with branching in $\mathbf {R}^n$
JO - Publications Mathématiques de l'IHÉS
PY - 2005
PB - Springer
VL - 101
SP - 209
EP - 241
AB - According to a theorem of Martio, Rickman and Väisälä, all nonconstant Cn/(n-2)-smooth quasiregular maps in Rn, n≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in R3. We prove that the order of smoothness is sharp in R4. For each n≥5 we construct a C1+ε(n)-smooth quasiregular map in Rn with nonempty branch set.
LA - eng
KW - space quasiregular mappings
UR - http://eudml.org/doc/104210
ER -

References

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