000			03825nam a22004935i 4500
001			978-0-8176-4693-6
003			DE-He213
005			20140220083227.0
007			cr nn 008mamaa
008			110907s2012 xxu| s |||| 0|eng d
020			_a9780817646936 _9978-0-8176-4693-6
024	7		_a10.1007/978-0-8176-4693-6 _2doi
050		4	_aQA331.7
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.94 _223
100	1		_aNapier, Terrence. _eauthor.
245	1	3	_aAn Introduction to Riemann Surfaces _h[electronic resource] / _cby Terrence Napier, Mohan Ramachandran.
264		1	_aBoston, MA : _bBirkhäuser Boston : _bImprint: Birkhäuser, _c2012.
300			_aXVII, 560p. 42 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aCornerstones
505	0		_aPreface -- Introduction -- Complex analysis in C -- Riemann Surfaces and the L2 \delta-Method for Scalar-Valued Forms -- The L2 \delta-Method in a Holomorphic Line Bundle -- Compact Riemann Surfaces -- Uniformization and Embedding of Riemann Surfaces.-Holomorphic Structures on Topological Surfaces -- Background Material on Analysis in Rn and Hilbert Space Theory -- Background Material on Linear Algebra -- Background Material on Manifolds -- Background Material on Fundamental Groups, Covering Spaces, and (Co)homology -- Background Material on Sobolev Spaces and Regularity -- References -- Notation Index -- Subject Index.
520			_aThis textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L² -method, a powerful technique used in the theory of several complex variables.  The work features a simple construction of a strictly subharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such as the Mittag-Leffler, Weierstrass, and Runge theorems; the Riemann−Roch theorem; the Serre duality and Hodge decomposition theorems; and the uniformization theorem. The book also contains treatments of other facts concerning the holomorphic, smooth, and topological structure of a Riemann surface, such as the biholomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schönflies theorem (and the Jordan curve theorem), and the existence of smooth structures on second countable surfaces.  Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises—many of which lead to further development of the theory—and  presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course.
650		0	_aMathematics.
650		0	_aGlobal analysis (Mathematics).
650		0	_aGlobal analysis.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
650	2	4	_aAnalysis.
700	1		_aRamachandran, Mohan. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817646929
830		0	_aCornerstones
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4693-6
912			_aZDB-2-SMA
999			_c100214 _d100214