國立虎尾科技大學 |

Harmonic mappings in the plane /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Harmonic mappings in the plane // Peter Duren.
作者:	Duren, Peter L.,
面頁冊數:	1 online resource (xii, 212 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Harmonic maps. -
電子資源:	https://doi.org/10.1017/CBO9780511546600
ISBN:	9780511546600 (ebook)

Harmonic mappings in the plane /
Duren, Peter L.,1935-

Harmonic mappings in the plane /Peter Duren. - 1 online resource (xii, 212 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;156. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511546600 (ebook)Subjects--Topical Terms:

685349
Harmonic maps.

LC Class. No.: QA614.73 / .D87 2004

Dewey Class. No.: 514/.74

Harmonic mappings in the plane /
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520 $a 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.
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