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20140310151441.0 |
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110518s2011 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9780817646226 |
|
978-0-8176-4622-6 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA331.7 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515.94 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Boston : |
| -- |
Birkhäuser Boston, |
| -- |
2011. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Greene, Robert E. |
| Relator term |
author. |
| 245 14 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
The Geometry of Complex Domains |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Robert E. Greene, Kang-Tae Kim, Steven G. Krantz. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XIV, 303p. 14 illus. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Progress in Mathematics ; |
| Volume number/sequential designation |
291 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
The geometry of complex domains is a subject with roots extending back more than a century, to the uniformization theorem of Poincaré and Koebe and the resulting proof of existence of canonical metrics for hyperbolic Riemann surfaces. In modern times, developments in several complex variables by Bergman, Hörmander, Andreotti-Vesentini, Kohn, Fefferman, and others have opened up new possibilities for the unification of complex function theory and complex geometry. In particular, geometry can be used to study biholomorphic mappings in remarkable ways. This book presents a complete picture of these developments. Beginning with the one-variable case—background information which cannot be found elsewhere in one place—the book presents a complete picture of the symmetries of domains from the point of view of holomorphic mappings. It describes all the relevant techniques, from differential geometry to Lie groups to partial differential equations to harmonic analysis. Specific concepts addressed include: covering spaces and uniformization; Bergman geometry; automorphism groups; invariant metrics; the scaling method. All modern results are accompanied by detailed proofs, and many illustrative examples and figures appear throughout. Written by three leading experts in the field, The Geometry of Complex Domains is the first book to provide systematic treatment of recent developments in the subject of the geometry of complex domains and automorphism groups of domains. A unique and definitive work in this subject area, it will be a valuable resource for graduate students and a useful reference for researchers in the field. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Global analysis (Mathematics). |
|
|---|
| Topical term or geographic name as entry element |
Differentiable dynamical systems. |
|
|---|
| Topical term or geographic name as entry element |
Differential equations, partial. |
|
|---|
| Topical term or geographic name as entry element |
Geometry. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Several Complex Variables and Analytic Spaces. |
|
|---|
| Topical term or geographic name as entry element |
Analysis. |
|
|---|
| Topical term or geographic name as entry element |
Dynamical Systems and Ergodic Theory. |
|
|---|
| Topical term or geographic name as entry element |
Geometry. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Kim, Kang-Tae. |
| Relator term |
author. |
|
|---|
| Personal name |
Krantz, Steven G. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9780817641399 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-0-8176-4622-6 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
