Abstract

Starting from [3], several authors have repeatedly posed the following problem (see [6, p. 126; 7] about this): Does the inequality (4) (and those equivalent to it) characterize the class E(k), i.e., is it also sufficient for the k-quasiconformal extendability of f? Pommerenke [2] has established that in each case the inequality (4) ensures the k'-quasiconformal extendability of f with k'~k. Kiihnau [6], using the connection between the Grunsky matrix and the least (nontrivial) Fredholm eigenvalue ~ of the curve f(Izl = I) (found in [8]), has shown that the posed problem Qhas a negative solution, namely: The function

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