000 02318nam a22003378i 4500
001 CR9780511546600
003 UkCbUP
005 20200124160233.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090508s2004||||enk o ||1 0|eng|d
020 _a9780511546600 (ebook)
020 _z9780521641210 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA614.73
_b.D87 2004
082 0 0 _a514/.74
_222
100 1 _aDuren, Peter L.,
_d1935-
_eauthor.
245 1 0 _aHarmonic mappings in the plane /
_cPeter Duren.
264 1 _aCambridge :
_bCambridge University Press,
_c2004.
300 _a1 online resource (xii, 212 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v156
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aHarmonic 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 _aHarmonic maps.
776 0 8 _iPrint version:
_z9780521641210
830 0 _aCambridge tracts in mathematics ;
_v156.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511546600
999 _c517797
_d517795