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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Construction of Hamilton sequences for certain Teichmüller mappings
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by Edgar Reich PDF
Proc. Amer. Math. Soc. 103 (1988), 789-796 Request permission

Abstract:

Suppose $\sup \{ |\iint _{\left | z \right | < 1} {\kappa (z)\varphi (z)dxdy|:\varphi (z)}$ analytic for $\left | z \right | < 1,\iint _{\left | z \right | < 1} {|\varphi (z)|dxdy = 1\} = {\text {ess}}\sup }\{ |\kappa (z)|:\left | z \right | < 1\}$. 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
  • © Copyright 1988 American Mathematical Society
  • 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