{"product_id":"an-introduction-to-riemann-surfaces-hardcover","title":"An Introduction to Riemann Surfaces - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eTerrence Napier\u003c\/b\u003e (Author), \u003cb\u003eMohan Ramachandran\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\\bar{\\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces. The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the \u003ci\u003eL\u003c\/i\u003e² -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. \u003c\/p\u003e\u003cp\u003eAlthough 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.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 560\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.25 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 28, 2011\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704563790131,"sku":"9780817646929","price":104.18,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/TGlRR3NPUmZVNzRlaWFJVUFNOVVlQT09.webp?v=1763359134","url":"https:\/\/www.vysn.com\/en-ca\/products\/an-introduction-to-riemann-surfaces-hardcover","provider":"VYSN","version":"1.0","type":"link"}