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200 10$aComplex analysis $ethe geometric viewpoint /$fSteven G. Krantz$b[electronic resource]
205   $a2nd ed.
210  1$aWashington :$cMathematical Association of America,$d2004.
215   $a1 online resource (xvii, 219 pages) $cdigital, PDF file(s)
225 1 $aThe Carus mathematical monographs ;$vno. 23
300   $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015).
311   $a0-88385-035-4 
320   $aIncludes bibliographical references (p. 209-211) and index.
327   $aPrincipal ideas of classical function theory -- Basic notions of differential geometry -- Curvature and applications -- Some new invariant metrics -- Introduction to the Bergman Theory -- A glimpse of several complex variables.
330   $aIn this second edition of a Carus Monograph Classic, Steven Krantz develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disc. He also introduces the Bergman kernal and metric and provides profound applications, some of them never having appeared before in print. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume.   This is the first and only book to describe the context, the background, the details, and the applications of Ahlfors's celebrated ideas about curvature, the Schwarz lemma, and applications in complex analysis. Beginning from scratch, and requiring only a minimal background in complex variable theory, this book takes the reader up to ideas that are currently active areas of study. Such areas include a) the Caratheodory and Kobayashi metrics, b) the Bergman kernel and metric, c) boundary continuation of conformal maps. There is also an introduction to the theory of several complex variables. Poincare?'s celebrated theorem about the biholomorphic inequivalence of the ball and polydisc is discussed and proved.
410  0$aCarus mathematical monographs ;$vno. 23.
606   $aFunctions of complex variables
606   $aGeometry, Differential
615  0$aFunctions of complex variables.
615  0$aGeometry, Differential.
676   $a515/.9
700   $aKrantz$b Steven G$g(Steven George),$f1951-$055961
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910822594503321
996   $aComplex analysis$979508
997   $aUNINA