Geometry of Complex Domains

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.

• Preface.- 1 Preliminaries.- 2 Riemann Surfaces and Covering Spaces.- 3 The Bergman Kernel and Metric.- 4 Applications of Bergman Geometry.- 5 Lie Groups Realized as Automorphism Groups.- 6 The Significance of Large Isotropy Groups.- 7 Some Other Invariant Metrics.- 8 Automorphism Groups and Classification of Reinhardt Domains.- 9 The Scaling Method, I.- 10 The Scaling Method, II.- 11 Afterword.- Bibliography.- Index.

From the reviews: "The book under review gives an excellent presentation of modern problems related to various characterizations of the holomorphic geometry of domains in Cn and complex manifolds. ... The book may be strongly recommended for researchers and Ph.D. students working in complex analysis." (Marek Jarnicki, Mathematical Reviews, Issue 2012 c)