Counterexamples Concerning Quasiconformal Extensions of Strongly Starlike Functions.

M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin( απ/2) on the whole complex plane $$ \bar {\Bbb C} $$ which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k ≤ α to the whole plane $$ \bar {\Bbb C} .$$ In this paper we will give a negative approach to the question. [ABSTRACT FROM AUTHOR]