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Field name	Details
Dewey Class	515.94
Title	An Introduction to Riemann Surfaces ([EBook]) / by Terrence Napier, Mohan Ramachandran.
Author	Napier, Terrence
Added Personal Name	Ramachandran, Mohan
Other name(s)	SpringerLink (Online service)
Publication	Boston, MA : Birkhäuser
Publication	, 2011
Physical Details	XVII, 560 pages, 42 illus. : online resource.
Series	Cornerstones
ISBN	9780817646936
Summary Note	This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the LÂ² -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 RiemannâRoch 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 Schönflie 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 exercisesâmany of which lead to further development of the theoryâand 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.:
Contents note	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 ofÂ Riemann Surfaces.-Holomorphic Structures on Topological Surfaces -- Background Material on Analysis in RnÂ 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4693-6
Links to Related Works	Subject References: Analysis . Differential equations, Partial . Global analysis . Global Analysis and Analysis on Manifolds . Global analysis (Mathematics) . Riemann surfaces . Several Complex Variables and Analytic Spaces . Authors: author . Napier, Terrence . Ramachandran, Mohan . Corporate Authors: SpringerLink (Online service) . Series: Cornerstones . Classification: 515.94 .

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An Introduction to Riemann Surfaces

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