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An Introduction to Riemann Surfaces (Cornerstones) by Terrence Napier downloads torrent download torrent

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Product Details:

Author(s): Terrence Napier

Category: Mathematics

Date: 2011-09-28

Pages: 577

Publisher: Birkhauser

Language: English

ISBN-10: 0817646922

ISBN-13: 9780817646929

Format: pdf

Book Description:

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L? -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 Schonflies 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 exercisesmany of which lead to further development of the theoryand 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.

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GO Downloads An Introduction to Riemann Surfaces (Cornerstones) by Terrence Napier

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