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On extremality of two connected locally extremal Beltrami coefficients

Published online by Cambridge University Press:  17 April 2009

Guowu Yao
Guowu Yao
Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China, e-mail: wallgreat@lycos.com
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Let Ω1 and Ω2 be two domains in the complex plane with a nonempty intersection. Suppose that μj are locally extremal Beltrami coefficients in Ωj (j = 1, 2) respectively. In 1980, Sheretov posed the problem: Will the coefficient μ defined by the condition μ(z) = μj(z) for z ∈ Ωj, j = 1, 2, be locally extremal in Ω1 ∪ Ω2? We give a counterexample to show that μ may not be locally extremal and not even be extremal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 37 - 40
Copyright
Copyright © Australian Mathematical Society 2005

References

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