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Quadratic Differentials: A Survey

In: Zum Werk Leonhard Eulers

Author

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  • Kurt Strebel

    (Universität Zürich, Mathematisches Institut)

Abstract

Quadratic differentials have become an important object in geometric function theory. They are connected with extremal quasiconformal mappings — with Teichmüller mappings [19], but also with the general problem of extremal qc. mappings [2], [10] -, with extremal problems for schlicht functions, like coefficient problems [18], [12], [6], with moduli problems [17], [13], extremal length [5] and even with measured foliations [4]. But they are not just tools: There is a geometric theory of quadratic differentials which has its own right of existence [6], [12, [16]. It is the purpose of this article to give a survey of the basic aspects of this theory as it has been developped by Teichmüller and numerous other authors in the years after their first appearance in Teichmüller’s famous mapping theorem.

Suggested Citation

  • Kurt Strebel, 1984. "Quadratic Differentials: A Survey," Springer Books, in: Eberhard Knobloch & Ilppo Simo Louhivaara & Jörg Winkler (ed.), Zum Werk Leonhard Eulers, pages 219-238, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7121-1_13
    DOI: 10.1007/978-3-0348-7121-1_13
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