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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
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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  • [1] W. K. Hayman and Edgar Reich, On Teichmüller mappings of the disk, Complex Variables 1 (1982), 1-12. MR 674357 (84e:30031)
  • [2] Edgar Reich and Kurt Strebel, Extremal quasiconformal mappings with given boundar values, Contributions to Analysis, a Collections of Papers Dedicated to Lipman Bers, Academic Press, New York, 1974, pp. 375-391. MR 0361065 (50:13511)
  • [3] Edgar Reich, Quasiconformal mappings of the disk with given boundary values, Lecture Notes in Math., vol. 505, Springer-Verlag, Berlin and New York, 1976, pp. 101-135. MR 0419758 (54:7776)
  • [4] G. C. Sethares, The extremal property of certain Teichmüller mappings, Comment. Math. Helv. 43 (1968), 98-119. MR 0228674 (37:4253)
  • [5] Kurt Strebel, Zur Frage der Eindeutigkeit extremaler quasikonformer Abbildungen des Einheitskreises, Comment. Math. Helv. 36 (1962), 306-323. MR 0164032 (29:1331)
  • [6] Marvin Ortel, Extremal quasiconformal mappings with angular dilatation, Indiana Univ. Math. J. 31 (1982), 435-447. MR 652827 (83f:30019)

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