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9780817646226
978-0-8176-4622-6
10.1007/978-0-8176-4622-6
doi
QA331.7
PBKD
bicssc
MAT034000
bisacsh
515.94
23
Greene, Robert E.
author.
The Geometry of Complex Domains
[electronic resource] /
by Robert E. Greene, Kang-Tae Kim, Steven G. Krantz.
Boston :
Birkhäuser Boston,
2011.
XIV, 303 p. 14 illus.
online resource.
text
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rdacontent
computer
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rdamedia
online resource
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rdacarrier
text file
PDF
rda
Progress in Mathematics ;
291
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.
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.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Dynamics.
Ergodic theory.
Functions of complex variables.
Geometry.
Mathematics.
Several Complex Variables and Analytic Spaces.
Analysis.
Dynamical Systems and Ergodic Theory.
Geometry.
Kim, Kang-Tae.
author.
Krantz, Steven G.
author.
SpringerLink (Online service)
Springer eBooks
Printed edition:
9780817641399
Progress in Mathematics ;
291
http://dx.doi.org/10.1007/978-0-8176-4622-6
ZDB-2-SMA
369953
369953
0
0
0
0
EBook
elib
elib
2018-01-15
2018-01-15
2018-01-15
EBOOK