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Quadratic Differentials with Closed Trajectories

  • Kurt Strebel
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 5)

Abstract

Quadratic differentials with closed trajectories were first considered by Teichmüller in his “Habilitationsschrift” [1] in the following example: two non overlapping punctured disks G′ and G″, with punctures at z =0 and z = ∞ respectively, which do not contain z = −1, have to be chosen in such a way that their reduced moduli M′ and M″ maximize the sum q 2 M′ + M″. The solution (“Extremalgebiete des speziellen Modulsatzes”, pg 33) is given by a quadratic differential with second order poles at 0 and ∞. For Riemann surfaces and finitely many punctures, the problem was solved by the author in [5] and [11], see §23 below.

Keywords

Conformal Mapping Existence Theorem Boundary Component Quadratic Differential Jordan Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Kurt Strebel
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

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