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Harmonic Mappings in the Plane
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Harmonic Mappings in the Plane

Harmonic Mappings in the Plane

Peter Duren - Collection Cambridge Tracts in Mathematics

212 pages, parution le 04/06/2004

Résumé

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.

Sommaire

  • Preliminaries
  • General properties of Harmonic Mappings
  • Harmonic Mappings onto Convex Regions
  • Harmonic Self-Mappings of the Disk
  • Harmonic Univalent Functions
  • Extremal Problems
  • Mapping Problems
  • Additional Topics
  • Minimal Surfaces
  • Curvature of Minimal Surfaces
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Caractéristiques techniques

  PAPIER
Éditeur(s) Cambridge University Press
Auteur(s) Peter Duren
Collection Cambridge Tracts in Mathematics
Parution 04/06/2004
Nb. de pages 212
Format 15,5 x 23,5
Couverture Relié
Poids 450g
Intérieur Noir et Blanc
EAN13 9780521641210
ISBN13 978-0-521-64121-0

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