Geodesic
Asymptotics of the coefficient quasiconformality, and the boundary behavior of a~mapping of a~ball
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 583-591

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It is shown that if a quasiconformal automorphism $f\colon B^n\to B^n$ of the unit ball in $\mathbf R^n$ $(n\geqslant 2)$ has coefficient of quasiconformality $K_f(r)=\sup\limits_{|x|\le r}k(f,x)$ in the ball of radius $r1$ with asymptotic growth such that $\int\limits^1K(r)\,dr\infty$, then it has a radial limit at almost every point of the boundary. This asymptotic growth of $K(r)$ is sharp in a certain sense. 
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     author = {M. N. Pantyukhina},
     title = {Asymptotics of the coefficient quasiconformality, and the boundary behavior of a~mapping of a~ball},
     journal = {Sbornik. Mathematics},
     pages = {583--591},
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     volume = {74},
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     year = {1993},
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     url = {http://geodesic.mathdoc.fr/item/SM_1993_74_2_a16/}
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M. N. Pantyukhina. Asymptotics of the coefficient quasiconformality, and the boundary behavior of a~mapping of a~ball. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 583-591. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a16/