English

Nonremovable sets for H\"older continuous quasiregular mappings in the plane

Analysis of PDEs 2007-05-23 v1

Abstract

We show that for any dimension t>2(1+alpha K)/(1+K) there exists a compact set E of dimension t and a function alpha-Holder continuous on the plane, which is K-quasiregular only outside of E. To do this, we construct an explicit K-quasiconformal mapping that gives, by one side, extremal dimension distortion on a Cantor-type set, and by the other, more Holder continuity than the usual 1/K.

Keywords

Cite

@article{arxiv.math/0604444,
  title  = {Nonremovable sets for H\"older continuous quasiregular mappings in the plane},
  author = {Albert Clop},
  journal= {arXiv preprint arXiv:math/0604444},
  year   = {2007}
}

Comments

17 pages, 3 figures

R2 v1 2026-07-22T17:34:46.545Z