000			02065cam a22002534a 4500
001			13250131
005			20250610111422.0
008			030624s2004 enka b 001 0 eng
020			_a9780521641210
040			_aCSL _cCSL
084			_aB6: 3N P4;1 NBHM _qCSL
100	1		_aDuren, Peter L., _eauthor
245	1	0	_aHarmonic mappings in the plane
260			_aCambridge : _bCambridge University Press, _c2004.
300			_axii, 212 p. : _bill. ; _c24 cm.
440		0	_aCambridge tracts in mathematics ; _v156 _9812352
504			_aIncludes bibliographical references (p. 201-209) and index.
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. _9812353
650		0	_aGeneral Properties of Harmonic Mappings _9812354
650		0	_aHarmonic Univalent Functions _9812355
650		0	_aCurvature of Minimal Surfaces _9812356
942			_2CC _n0 _cTEXL _hB6: 3N P4;1 NBHM
999			_c1431549 _d1431549