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3. Moduli in Extremal Problems for Conformal Mapping

  • Alexander Vasil’evEmail author
Chapter
  • 291 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1788)

Abstract

  • 3.1 Classical extremal problems for univalent functions
    • 3.1.1 Koebe set, growth, distortion

    • 3.1.2 Lower boundary curve for the range of (|f(z)|,|f’(z)|)

    • 3.1.3 Special moduli

    • 3.1.4 Upper boundary curve for the range of (|f(z)|,|f’(z)|)

  • 3.2 Two-point distortion for univalent functions
    • 3.2.1 Lower boundary curve for the range of (|f(r1)|,|f(r2)|) in S R

    • 3.2.2 Special moduli

    • 3.2.3 Upper boundary curve for the range of (|f(r1)|,|f(r2)|) in S R

    • 3.2.4 Upper boundary curve for the range of (|f(r1)|, |f(r2)|) in S

  • 3.3 Bounded univalent functions
    • 3.3.1 Elementary estimates

    • 3.3.2 Boundary curve for the range of (|f(z)|,|f’(z)|) in B s (b)

  • 3.4 Montel functions
    • 3.4.1 Covering theorems

    • 3.4.2 Distortion at the points of normalization

    • 3.4.3 The range of (|f(r)|,|f’(r)|) in \(M_R(\omega )\)

  • 3.5 Univalent functions with the angular derivatives
    • 3.5.1 Estimates of the angular derivatives

    • 3.5.2 The range of (|f(r)|, |f’(0)|)

Mathematics Subject Classification (2000):

30C35 30C55 30C62 30C75 30F10 30F60 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2002

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa María Casilla110-V ValparaísoChile

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