[8] Sur un théorème de la représentation conforme

  • Peter Duren
Part of the Contemporary Mathematicians book series (CM)


Schiffer presented his celebrated method of boundary variation in his doctoral thesis of 1939 at the Hebrew University, “Conformal Representation and Univalent Functions” (in Hebrew), under the supervision of Michael Fekete. An announcement had appeared in [3], and a detailed account was first published in [5]. The method was applied in [4] to an extremal problem for transfinite diameter. The papers [6, 8] further demonstrated the power of the variational method with applications to problems in function theory.


Extremal Problem Boundary Variation Quadratic Differential Extremal Function Geometric Function Theory 
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  1. [B]
    Louis de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137–152.MathSciNetCrossRefMATHGoogle Scholar
  2. [CL]
    Douglas M. Campbell and Jack Lamoreaux, Continua in the plane with limit directions, Pacific J. Math. 74 (1978), 37–46.MathSciNetCrossRefMATHGoogle Scholar
  3. [D]
    Peter L. Duren, Univalent Functions, Springer-Verlag, 1983.Google Scholar
  4. [FP]
    Carl H. FitzGerald and Ch. Pommerenke, The de Branges theorem on univalent functions, Trans. Amer. Math. Soc. 290 (1985), 683–690.MathSciNetCrossRefMATHGoogle Scholar
  5. [G]
    G. M. Goluzin, On p-valent functions, Mat. Sb. 8 (50) (1940), 277–284 (in Russian).MATHGoogle Scholar
  6. [HJ]
    U. S. Haslam-Jones, Tangential properties of a plane set of points, Quart. J. Math. 7 (1936), 116–123.CrossRefGoogle Scholar
  7. [Le]
    Olli Lehto, Anwendung orthogonaler Systeme auf gewisse funktionentheoretische Extremal- und Abbildungsprobleme, Ann. Acad. Sci. Fenn. Ser. A I Math.–Phys. 1949, no. 59.Google Scholar
  8. [Lo]
    Karl Löwner (Charles Loewner), Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, I , Math. Ann. 89 (1923), 103–121.Google Scholar
  9. [M]
    F. Marty, Sur le module des coefficients de MacLaurin d’une fonction univalente, C. R. Acad. Sci. Paris 198 (1934), 1569–1571.Google Scholar
  10. [S]
    Glenn Schober, Univalent Functions – Selected Topics, Lecture Notes in Math. 478, Springer-Verlag, 1975. Peter Duren Google Scholar

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Peter Duren
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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