| ON A PROBLEM OF E.REICH |
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| 作者姓名： | 吴泽民 |
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| 作者单位： | 福建泉州师专数学系!邮编362000 |
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| 基金项目： | National Natural Science foundation ofChina!( No.195310 60 )，Doctor Fundsof National Education Committec!( 970 2 4 811) |
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| 摘 要： | IntroductionLetΦ0 ( z) be a complex- valued measurable func-tion defined in a regionΩ of the complex plainC,Φ0 ( z)≠ 0 ,∞ ,a.e.,and let k be a constant0≤ k<1 .A quasiconformal mapping w=f( z) ofΩ will be said to be Teichmüller type if f hascomplex dilatationχ( z) =f-z /fz =kφ0 ( z) /|φ0 ( z) |, z∈Ω In particular,ifΦ0 ( z) is holomorphic inΩ,then f is called a Teichmüller mapping. We are interested in whether f is a bothTeichmüller mapping and uniquely extremalmapping a…
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| 关 键 词： | quasiconformal mappings uniquely extremal mapping Teichmüller mapping Document code:A |
ON A PROBLEM OF E. REICH |
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| WU Ze-min.ON A PROBLEM OF E.REICH[J].Journal of Shanghai Jiaotong university,2000,5(2). |
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| Authors: | WU Ze-min |
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| Abstract: | In 1981, E. Reich established a theorem which stated a sufficient condition for a quasiconformal mapping to be a unique extremal mapping with the given boundary value, and asked whether or not such a uniquely extremal mapping was a Teichmuller mapping in his remark. In this paper, the above open problem was solved and consequently the theorem was strengthened. |
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| Keywords: | quasiconformal mappings uniquely extremal mapping Teichmuller mapping |
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