Complex Analysis: The Geometric Viewpoint

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Mathematical Association of America, 2004 - Mathematics - 219 pages
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In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, 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 disk. He also introduces the Bergmann kernel and metric and provides profound applications, some of which have never appeared in print before. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight. The climax of the book is an introduction to several complex variables from the geometric viewpoint. Poincaré's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved.

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About the author (2004)

Steven G. Krantz was born in San Francisco, California in 1951. He received the B.A. degree from the University of California at Santa Cruz in 1971 and the Ph.D. from Princeton University in 1974. He is the recipient of the Chauvenet Prize and Beckenbach Book Award, both from the MAA. He also has received the UCLA Alumni Foundation Distinguished Teaching Award and Outstanding Academic Book Award from the Current Review for Academic Libraries. Krantz has authored 45 books and 120 research papers. He has directed 14 Ph.D. theses.

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