The Geometry of Complex Domains

Front Cover
Birkhäuser Boston, May 30, 2011 - Mathematics - 303 pages
0 Reviews
Reviews aren't verified, but Google checks for and removes fake content when it's identified

This highly original work, written by the creators of the multivariable theory of automorphisms, is a rich tapestry of themes and concepts, and a comprehensive treatment of an important area of mathematics. From Poincaré's work on biholomorphic inequivalence in 1906, it became clear that the structures of the automorphism groups of domains in multi-dimensional complex space are more complex, and more interesting, than those in the complex plane. The authors build on this theme and trace the evolution of the classical theory to the modern theory, which is today a cornerstone of geometric analysis.

The text begins with an introductory chapter on the concept of an automorphism group in which the theory in one complex variable is presented, emphasizing the classical ideas of Schwarz, Jobe, and others. Also examined is the theory of planar domains of multiple but finite connectivity, principally develped by Heins in the 1940s and 1950s. The authors treatment progresses to the theory in several complex variables with the so-called "classical domains" of E. Cartan, the Siegel domains of type I, II, and III, and the more modern theory of automorphism groups of smoothly bounded domains.

What people are saying - Write a review

We haven't found any reviews in the usual places.

Other editions - View all

About the author (2011)

Steven G. Krantz received the B.A. degree from the University of California at Santa Cruz and the Ph.D. from Princeton University. He has taught at UCLA, Princeton, Penn State, and Washington University, where he has most recently served as Chair of the Mathematics Department.

Krantz has directed 18 Ph.D. Students and 9 Masters students, and is winner of the Chauvenet Prize and the Beckenbach Book Award. He edits six journals and is Editor-in-Chief of three.

A prolific scholar, Krantz has published more than 55 books and more than 160 academic papers.

Bibliographic information