An Introduction to Infinite-Dimensional Differential Geometry PDF Download
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Author: Alexander Schmeding
Publisher: Cambridge University Press
ISBN: 1009089307
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.
Author: Alexander Schmeding
Publisher: Cambridge University Press
ISBN: 1009089307
Category : Mathematics
Languages : en
Pages : 284
Get Book
Book Description
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.
Author: A. Schmeding
Publisher:
ISBN: 9781009091251
Category : MATHEMATICS
Languages : en
Pages : 0
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Book Description
"This text introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, exploring modern applications. Emphasising connections to finite-dimensional geometry, it is accessible to graduate students, as well as researchers wishing to learn about the subject. Also available as Open Access on Cambridge Core"--
Author: Alexander Schmeding
Publisher: Cambridge University Press
ISBN: 1316514889
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.
Author: Andreas Kriegl
Publisher: American Mathematical Soc.
ISBN: 0821807803
Category : Global analysis (Mathematics).
Languages : en
Pages : 631
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Book Description
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461205417
Category : Mathematics
Languages : en
Pages : 553
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Book Description
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Author: J.K. Hale
Publisher: Springer Science & Business Media
ISBN: 1475744935
Category : Mathematics
Languages : en
Pages : 203
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Book Description
Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author: J. Margalef-Roig
Publisher: Elsevier
ISBN: 0444884343
Category : Mathematics
Languages : en
Pages : 622
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Book Description
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Author: Serge Lang
Publisher: Springer
ISBN: 9781441930194
Category : Mathematics
Languages : en
Pages : 250
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Book Description
Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics
Author: Giuseppe Da Prato
Publisher: Springer Science & Business Media
ISBN: 3540290214
Category : Mathematics
Languages : en
Pages : 217
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Book Description
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
Author: Jack K. Hale
Publisher: Springer Science & Business Media
ISBN: 0387228969
Category : Mathematics
Languages : en
Pages : 286
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Book Description
State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications
