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On the Extremality of Quasiconformal Mappings and Quasiconformal Deformations

Shen Yu-Liang
Proceedings of the American Mathematical Society
Vol. 128, No. 1 (Jan., 2000), pp. 135-139
Stable URL: http://www.jstor.org/stable/119393
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Extremality of Quasiconformal Mappings and Quasiconformal Deformations
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Abstract

Given a family of quasiconformal deformations F(w, t) such that $\overline{\partial}$F has a uniform bound M, the solution f(z, t) (f(z, 0) = z) of the Lowner-type differential equation dw/dt = F(w, t) is an e2Mt-quasiconformal mapping. An open question is to determine, for each fixed t > 0, whether the extremality of f(z, t) is equivalent to that of F(w, t). The note gives this a negative approach in both directions.

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