Format:
1 Online-Ressource (xii, 212 pages)
,
digital, PDF file(s).
ISBN:
9780511546600
Series Statement:
Cambridge tracts in mathematics 156
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521641210
Additional Edition:
ISBN 9780521641210
Additional Edition:
Erscheint auch als Duren, Peter L., 1935 - 2020 Harmonic mappings in the plane Cambridge [u.a.] : Cambridge University Press, 2004 ISBN 9780521641210
Additional Edition:
ISBN 0521641217
Additional Edition:
Print version ISBN 9780521641210
Language:
English
Subjects:
Mathematics
Keywords:
Harmonische Abbildung
;
Minimalfläche
DOI:
10.1017/CBO9780511546600
Author information:
Duren, Peter L. 1935-2020
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