000			03824nam a22005295i 4500
001			978-0-8176-4622-6
003			DE-He213
005			20140220083711.0
007			cr nn 008mamaa
008			110518s2011 xxu| s |||| 0|eng d
020			_a9780817646226 _9978-0-8176-4622-6
024	7		_a10.1007/978-0-8176-4622-6 _2doi
050		4	_aQA331.7
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.94 _223
100	1		_aGreene, Robert E. _eauthor.
245	1	4	_aThe Geometry of Complex Domains _h[electronic resource] / _cby Robert E. Greene, Kang-Tae Kim, Steven G. Krantz.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXIV, 303p. 14 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Mathematics ; _v291
505	0		_aPreface -- 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			_aThe 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	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650		0	_aDifferentiable dynamical systems.
650		0	_aDifferential equations, partial.
650		0	_aGeometry.
650	1	4	_aMathematics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aAnalysis.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aGeometry.
700	1		_aKim, Kang-Tae. _eauthor.
700	1		_aKrantz, Steven G. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817641399
830		0	_aProgress in Mathematics ; _v291
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4622-6
912			_aZDB-2-SMA
999			_c105076 _d105076