Complex Analysis: The Geometric Viewpoint

ISBN-13: 9780883850350 / Angielski / Twarda / 2004 / 234 str.

Steven G. Krantz

Opis

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. Poincare's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved."

Recenzje

'In five very nicely written chapters this book gives an introduction to the approach to function theory via Riemannian geometry. Very little function-theoretic background is needed and no knowledge whatsoever of differential geometry is assumed.' Mathematical Reviews

Spis treści

Preface; Principal ideas of classical function theory; 1. Basic notions of differential geometry; 2. Curvature and applications; 3. Some new invariant metrics; 4. Introduction to the Bergmann theory; 5. A glimpse of several complex variables; 6. Appendix; Symbols; References; Index.