Nonremovable sets for Hölder continuous quasiregular mappings in the plane

Details Nonremovable sets for Hölder continuous quasiregular mappings in the plane Nonremovable sets for Hölder continuous quasiregular mappings in the plane

2006-04-20

arxiv.org/abs/math/0604444v1

Mathematics

Analysis of PDEs

17 pages, 3 figures

Scientific paper

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.

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