大葉大學圖書館 |

Harmonic mappings in the plane /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	514/.74
書名/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.
ISBN:	9780511546600 (ebook)
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1017/CBO9780511546600

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 ;169..

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:

517735
Harmonic maps.

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

Dewey Class. No.: 514/.74

Harmonic mappings in the plane /
LDR:02157nam a22002898i 4500 001 448426
003 UkCbUP
005 20151005020621.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 161201s2004||||enk o ||1 0|eng|d
020 $a 9780511546600 (ebook)
020 $z 9780521641210 (hardback)
035 $a CR9780511546600
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA614.73 $b .D87 2004
082 0 0 $a 514/.74 $2 22
100 1 $a Duren, Peter L., $d 1935- $e author. $3 643061
245 1 0 $a Harmonic mappings in the plane / $c Peter Duren.
264 1 $a Cambridge : $b Cambridge University Press, $c 2004.
300 $a 1 online resource (xii, 212 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
490 1 $a Cambridge tracts in mathematics ; $v 156
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
650 0 $a Harmonic maps. $3 517735
776 0 8 $i Print version: $z 9780521641210
830 0 $a Cambridge tracts in mathematics ; $v 169. $3 642585
856 4 0 $u http://dx.doi.org/10.1017/CBO9780511546600