On mean quasiconformal mappings
Let \(H^\Phi\) be the set of all orientation preserving homeomorphisms \(f:\overline{C}\to \overline{C}\) of the Sobolev space \(W_{1,\text{loc}}^1\) with the normalization \(f(0)=0\), \(f(1)=1\) and \(f(\infty)=\infty\) and the integral condition on the dilatation \(p(z)\) \[ \iint_C \Phi(p(z))dx dy\leq 1. \] The author proves a necessary and sufficient compactness result and a compactification result for the set \(H^\Phi\) in the case of a function \(\Phi\) with exponential growth.
scientific article; zbMATH DE number 1023970
scientific article