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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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Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.

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Geometry and Analysis on Manifolds:In Memory of Professor Shoshichi Kobayashi. Softcover reprint of the original 1st ed. 2015

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Geometry and Analysis on Manifolds:Proceedings of the 21st International Taniguchi Symposium held at Katata, Japan, Aug. 23-29 and the Conference held at Kyoto, Aug. 31 - Sep. 2, 1987. Auflage 1988

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63,99 € *

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This book presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. Exercises are included throughout, which makes this text ideal for a one- or two-semester graduate course. 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. 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. 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.

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Gebraucht - Gut Bibliotheksexemplar, gestempelt, Aufkleber, altersgemäßer Zustand, Versand BüchersendungAnalysis; Manifolds and Physics, Part 1: BasicsZustand: Gebraucht - GutEinbandart: Gebundene AusgabeISBN-13: 9780444860170Verlag: North

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(100,99 € / in stock)

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(100,99 € / in stock)

Geometry and Analysis on Manifolds:In Memory of Professor Shoshichi Kobayashi Progress in Mathematics. Auflage 2015

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This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to R n to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.

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Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.

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