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

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.