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Author: Jürgen Eichhorn
Publisher: Nova Publishers
ISBN: 9781600215636
Category : Mathematics
Languages : en
Pages : 664
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Book Description
Global analysis is the analysis on manifolds. Since the middle of the sixties there exists a highly elaborated setting if the underlying manifold is compact, evidence of which can be found in index theory, spectral geometry, the theory of harmonic maps, many applications to mathematical physics on closed manifolds like gauge theory, Seiberg-Witten theory, etc. If the underlying manifold is open, i.e. non-compact and without boundary, then most of the foundations and of the great achievements fail. Elliptic operators are no longer Fredholm, the analytical and topological indexes are not defined, the spectrum of self-adjoint elliptic operators is no longer discrete, functional spaces strongly depend on the operators involved and the data from geometry, many embedding and module structure theorems do not hold, manifolds of maps are not defined, etc. It is the goal of this new book to provide serious foundations for global analysis on open manifolds, to discuss the difficulties and special features which come from the openness and to establish many results and applications on this basis.
Author: Jürgen Eichhorn
Publisher: Nova Publishers
ISBN: 9781600215636
Category : Mathematics
Languages : en
Pages : 664
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Book Description
Global analysis is the analysis on manifolds. Since the middle of the sixties there exists a highly elaborated setting if the underlying manifold is compact, evidence of which can be found in index theory, spectral geometry, the theory of harmonic maps, many applications to mathematical physics on closed manifolds like gauge theory, Seiberg-Witten theory, etc. If the underlying manifold is open, i.e. non-compact and without boundary, then most of the foundations and of the great achievements fail. Elliptic operators are no longer Fredholm, the analytical and topological indexes are not defined, the spectrum of self-adjoint elliptic operators is no longer discrete, functional spaces strongly depend on the operators involved and the data from geometry, many embedding and module structure theorems do not hold, manifolds of maps are not defined, etc. It is the goal of this new book to provide serious foundations for global analysis on open manifolds, to discuss the difficulties and special features which come from the openness and to establish many results and applications on this basis.
Author: Jurgen Eichhorn
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Andreas Kriegl
Publisher: American Mathematical Soc.
ISBN: 0821807803
Category : 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: Demeter Krupka
Publisher: Elsevier
ISBN: 0080556736
Category : Mathematics
Languages : en
Pages : 1243
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Book Description
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Author: Jrgen Eichhorn
Publisher: World Scientific
ISBN: 981277145X
Category : Mathematics
Languages : en
Pages : 353
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Book Description
For closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Ilka Agricola
Publisher: American Mathematical Soc.
ISBN: 0821829513
Category : Mathematics
Languages : en
Pages : 362
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Book Description
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.
Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 0486152294
Category : Mathematics
Languages : en
Pages : 20
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Book Description
This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 038721772X
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: Jürgen Eichhorn
Publisher: Nova Science Publishers
ISBN: 9781536129397
Category : Categories (Mathematics)
Languages : en
Pages : 0
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Book Description
A certain classification of open manifolds has been a continuous problem in geometry, topology and global analysis. The background for this is the fact that in any dimension greater than one, there are innumerous homotopy types. A solution to this problem seemed almost hopeless. In this monograph, the author offers an approach by decomposing the classification into two fundamental steps. This book introduces certain uniform structures in the set of all proper metric spaces under consideration (complexes, Riemannian manifolds, etc.), then considers the components of this uniform space by classifying the components adapted by homology theories (Gromov-Hausdorff and Lipschitz cohomology). The author then moves on to classifying the elements inside a component. For the second step, a geometric bordism theory for open manifolds and describes geometric generators is introduced. The main achievements include the invariance of a spectral gap under uniform homotopy equivalences and the vanishing of the K-theoretic signature in the geometric bordism theory. Concerning surgery, the absolutely fundamental achievements of Maumary and Taylor are included. Repeated motivations and explanations should make this monograph fairly legible to a vast audience. In particular, guidance is given on the ways in which supply chains can be diagnosed for vulnerabilities and the remedies that may be applied. One such countermeasure, virtual dualization, is explained in detail as a means for achieving both supply chain robustness and competitiveness for complex products that require intense coordination in their design and production. A common theme that runs throughout the chapter is the importance of building trust among the participants in a supply chain.