An Introduction to Riemann Surfaces

This 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 co...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Napier, Terrence (Συγγραφέας), Ramachandran, Mohan (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
Σειρά:Cornerstones
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Napier, Terrence.  |e author. 
245 1 3 |a An Introduction to Riemann Surfaces  |h [electronic resource] /  |c by Terrence Napier, Mohan Ramachandran. 
264 1 |a Boston, MA :  |b Birkhäuser Boston :  |b Imprint: Birkhäuser,  |c 2012. 
300 |a XVII, 560 p. 42 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Cornerstones 
505 0 |a Preface -- 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 |a This 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 |a Mathematics. 
650 0 |a Mathematical analysis. 
650 0 |a Analysis (Mathematics). 
650 0 |a Global analysis (Mathematics). 
650 0 |a Manifolds (Mathematics). 
650 0 |a Functions of complex variables. 
650 1 4 |a Mathematics. 
650 2 4 |a Several Complex Variables and Analytic Spaces. 
650 2 4 |a Global Analysis and Analysis on Manifolds. 
650 2 4 |a Analysis. 
700 1 |a Ramachandran, Mohan.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9780817646929 
830 0 |a Cornerstones 
856 4 0 |u http://dx.doi.org/10.1007/978-0-8176-4693-6  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)