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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2006, Vol. 7 Issue (Supplement 2): 198-202    DOI: 10.1631/jzus.2006.AS0198
Original Paper     
A problem on extremal quasiconformal extensions
Chen Zhi-Guo
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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Abstract  In this paper we give a short survey on a problem on extremal quasiconformal extensions. It had been a conjecture for a long time that the dilatations K0(h) and K1(h) are equal before Anderson and Hinkkanen disproved this by constructing concrete examples of a family of affine mappings of some parallelograms. The problem also engendered many interesting results. At the end of the current paper, we discuss relationships among K0(h), H(h) and K1(h) as a concluding remark.

Key words： Quasisymmetric mapping      Extremal quasiconformal mapping      Universal Teichmüller space      Non-Strebel point     
Received: 20 November 2005     
CLC:  O174.5  
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Chen Zhi-Guo. A problem on extremal quasiconformal extensions. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(Supplement 2): 198-202.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2006.AS0198     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2006/V7/ISupplement 2/198

[1] CHEN Zhi-guo. Riemann surface with almost positive definite metric*[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 7): 23-.
[2] Chen Zhi-Guo. A problem on extremal quasiconformal extensions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 0, (): 198-202.