ASYMPTOTICS OF THE COEFFICIENT OF QUASICONFORMALITY, AND THE BOUNDARY-BEHAVIOR OF A MAPPING OF A BALL

It is shown that if a quasiconformal automorphism f : B(n) --> B(n) of the unit ball in R(n) (n greater-than-or-equal-to 2) has coefficient of quasiconformality K(f)(r) = sup(Absolute value of x less-than-or-eq ual-to r) k(f, x) in the ball of radius r < 1 with asymptotic growth s uch that integral1 K(f)(r) dr < infinity, then it has a radial limit a t almost every point of the boundary. This asymptotic growth of K(f)(r ) is sharp in a certain sense.