ALMOST QUASICONFORMAL MAPPINGS WITH GIVEN BOUNDARY VALUES AND A COMPLEX DILATATION BOUND
Citation：
Lai Wancai.ALMOST QUASICONFORMAL MAPPINGS WITH GIVEN BOUNDARY VALUES AND A COMPLEX DILATATION BOUND[J].Chinese Annals of Mathematics B,1988,9(2):239~249
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Authors：
Lai Wancai;
Abstract：
In the extremal problems of qnasiconformal mappings with given boundary values and a complex dilatation bound which are discussed by Reich, the extremal mapping is required to have no conformal point set of positive measure on the defining set $T$ of the complex dilatation bound $\[b(w)\]$. Under the additional assumptions that $\[\bar T/T\]$ has measure zero and $\[b(w)\]$ is continuous a.e. Chen Jixiu proved that the extremal mapping may be relaxed to have a conformal positive measure set and a finite number of singularity points on $T$. In this paper the author proves that when the additional assumptions are given up,
the same relaxations still hold and the extremal mapping is also allowed to have a countable number of singularity points on $T$.
