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Cambridge Tracts in Mathematics Ser.: Harmonic Mappings in the Plane by Peter Duren (2004, Hardcover)

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HARMONIC MAPPINGS IN THE PLANE, Hardcover by Duren, Peter L., ISBN 0521641217, ISBN-13 9780521641210, Brand New, Free shipping in the US Duran (mathematics, U. of Michigan) examines these univalent complex-valued harmonic functions of a complex variable, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Duran's topics include general properties of harmonic mappings, harmonic mappings into convex regions, harmonic self-mappings of the disk, harmonic univalent functions, external problems, mapping problems, minimal surfaces and curvature of minimal surfaces, with particular attention to the Weierstrass-Enneper representation. Readers may wish to be prepared in complex analysis. Annotation ©2005 Book News, Inc., Portland, OR ()

About this product

Product Identifiers

PublisherCambridge University Press

ISBN-100521641217

ISBN-139780521641210

eBay Product ID (ePID)1944952

Product Key Features

Number of Pages226 Pages

LanguageEnglish

Publication NameHarmonic Mappings in the Plane

SubjectComplex Analysis, Mathematical Analysis

Publication Year2004

TypeTextbook

Subject AreaMathematics

AuthorPeter Duren

SeriesCambridge Tracts in Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.6 in

Item Weight17.6 Oz

Item Length9 in

Item Width6 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2003-056516

Dewey Edition22

Reviews'This book is devoted to the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.' Monatshefte f r Mathematik, 'Those who are sensible to the beauty of complex functions and Riemann surfaces will certainly enjoy reading this nicely written ... book.' Mathematical Geology, ‘For all students in this filed Duren's book will be essential reading. it will also be the classic reference book in this area.‘Proceedings of the Edinburgh Mathematical Society, 'This book is devoted to the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.' Monatshefte für Mathematik, ‘This book is devoted to the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.‘Monatshefte für Mathematik, 'Those who are sensible to the beauty of complex functions and Riemann surfaces will certainly enjoy reading this nicely written â€¦ book.' Mathematical Geology, 'For all students in this filed Duren's book will be essential reading. it will also be the classic reference book in this area.' Proceedings of the Edinburgh Mathematical Society, 'This book is devoted to the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces.' Monatshefte fr Mathematik

Series Volume NumberSeries Number 156

IllustratedYes

Dewey Decimal514/.74

Table Of Content1. Preliminaries; 2. Local properties of harmonic mappings; 3. Harmonic mappings onto convex regions; 4. Harmonic self-mappings of the disk; 5. Harmonic univalent functions; 6. Extremal problems; 7. Mapping problems; 8. Additional topics; 9. Minimal surfaces; 10. Curvature of minimal surfaces; Appendix; References.

SynopsisThis first comprehensive account of the theory of planar harmonic mappings, meant for non-specialists, treats both the generalizations of univalent analytic functions and the connections with minimal surfaces. Included are background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation., 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., 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. It contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It introduces non-specialists to a beautiful area of complex analysis and geometry.

LC Classification NumberQA614.73 .D87 2004