Counterexamples Concerning Quasiconformal Extensions of Strongly Starlike Functions |
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Authors: | Yu Liang Shen |
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Affiliation: | (1) Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China |
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Abstract: | 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 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 In this paper we will give a negative approach to the question. This research was supported by NNSF of China (Grant No. 10231040) and NCET (06-0504) |
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Keywords: | strongly starlike function quasiconformal extension Schwarzian derivative Teichmiiller mapping |
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