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Construction of Hamilton sequences for certain Teichmüller mappings


Author: Edgar Reich
Journal: Proc. Amer. Math. Soc. 103 (1988), 789-796
MSC: Primary 30C60; Secondary 30C75
DOI: https://doi.org/10.1090/S0002-9939-1988-0947659-2
MathSciNet review: 947659
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Abstract: Suppose $ \sup \{ \vert\iint_{\left\vert z \right\vert < 1} {\kappa (z)\varphi (z)dxdy\vert:\varphi (z)}$ analytic for $ \left\vert z \right\vert < 1,\iint_{\left\vert z \right\vert < 1} {\vert\varph... ...1\} = {\text{ess}}\sup }\{ \vert\kappa (z)\vert:\left\vert z \right\vert < 1\} $. The question of constructive determination of extremal sequences $ \{ \varphi_n \}$ is considered for some classes of functions $ \kappa(z)$ that arise in connection with plane quasiconformal mappings. For example, such a sequence $ \{ \varphi_n \}$ is constructed explicitly for the $ \kappa (z)$ that arises in connection with the affine stretch of Strebel's chimney domain.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947659-2
Article copyright: © Copyright 1988 American Mathematical Society

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