From Holomorphic Functions to Complex Manifolds

Author: Klaus Fritzsche,Hans Grauert

Publisher: Springer Science & Business Media

ISBN: 146849273X

Category: Mathematics

Page: 398

View: 4222

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This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
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Selected Papers I

Author: Hans Grauert

Publisher: Springer

ISBN: 9783662449356

Category: Mathematics

Page: 439

View: 6385

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Hans Grauert was one of the world's leading mathematicians in the field of Several Complex Variables; he not only shaped the development of this area decisively but was also responsible for some of its most important results. This representative selection of mathematical papers exhibits Grauert's influential research and reflects two decades of excellence. In this edition, each paper has been augmented by a detailed commentary, thus offering a comprehensive survey of the development of this fascinating subject from its beginnings in Münster and Göttingen. Hans Grauert may be regarded as a direct successor of Gauss, holding a chair at Göttingen that before him was held by Siegel, Weyl, Hilbert, Riemann and Gauss.
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Differential Analysis on Complex Manifolds

Author: Raymond O. Wells

Publisher: Springer Science & Business Media

ISBN: 0387738916

Category: Mathematics

Page: 304

View: 6173

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A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
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Introduction to Holomorphic Functions of Several Variables

Author: R.C. Gunning

Publisher: CRC Press

ISBN: 9780534133085

Category: Mathematics

Page: 198

View: 2823

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Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
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Differential Analysis on Complex Manifolds

Author: R. O. Wells

Publisher: Springer Science & Business Media

ISBN: 147573946X

Category: Mathematics

Page: 262

View: 8923

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In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of certain developments in the field during the decades since the book first appeared. From reviews of the 2nd Edition: "..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work." - Nigel Hitchin, Bulletin of the London Mathematical Society "Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material." - Daniel M. Burns, Jr., Mathematical Reviews
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Holomorphic Functions of Several Variables

An Introduction to the Fundamental Theory

Author: Ludger Kaup,Burchard Kaup

Publisher: Walter de Gruyter

ISBN: 3110838354

Category: Mathematics

Page: 363

View: 4498

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
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Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4219

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Lectures on Riemann Surfaces

Author: Otto Forster

Publisher: Springer Science & Business Media

ISBN: 1461259614

Category: Mathematics

Page: 256

View: 1559

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This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS
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Complex Analysis

In the Spirit of Lipman Bers

Author: Rubí E. Rodríguez,Irwin Kra,Jane P. Gilman

Publisher: Springer Science & Business Media

ISBN: 1441973230

Category: Mathematics

Page: 306

View: 960

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The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.
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