Introduction To Global Analysis
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Introduction To Global Analysis
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Author : Donald W. Kahn
language : en
Publisher:
Release Date : 1980-01-01
Introduction To Global Analysis written by Donald W. Kahn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.
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.
Introduction To Global Analysis
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Author : Floris Takens
language : en
Publisher:
Release Date : 1973
Introduction To Global Analysis written by Floris Takens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Differential equations categories.
Introduction To Global Analysis Minimal Surfaces In Riemannian Manifolds
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Author : John Douglas Moore
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-15
Introduction To Global Analysis Minimal Surfaces In Riemannian Manifolds written by John Douglas Moore and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Electronic books categories.
During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces. This book is based on lecture notes for graduate courses on “Topics in Differential Geometry”, taught by the author over several years. The reader is assumed to have taken basic graduate courses in differential geometry and algebraic topology.
Introduction To Global Analysis
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Author : Donald W. Kahn
language : en
Publisher: Courier Corporation
Release Date : 2007-03-29
Introduction To Global Analysis written by Donald W. Kahn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-29 with Mathematics categories.
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.
Critical Point Theory In Global Analysis And Differential Topology
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Author :
language : en
Publisher: Academic Press
Release Date : 2014-05-14
Critical Point Theory In Global Analysis And Differential Topology written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Mathematics categories.
Critical Point Theory in Global Analysis and Differential Topology
Introduction To Global Analysis
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Author : Donald W. Kahn
language : en
Publisher: Courier Corporation
Release Date : 2013-11-07
Introduction To Global Analysis written by Donald W. Kahn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-07 with Mathematics categories.
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.
Critical Point Theory In Global Analysis And Differential Topology
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Author :
language : en
Publisher:
Release Date : 1969
Critical Point Theory In Global Analysis And Differential Topology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Critical point categories.
Global And Stochastic Analysis With Applications To Mathematical Physics
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Author : Yuri E. Gliklikh
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-07
Global And Stochastic Analysis With Applications To Mathematical Physics written by Yuri E. Gliklikh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-07 with Mathematics categories.
Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.
Global Analysis On Foliated Spaces
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Author : Calvin C. Moore
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Global Analysis On Foliated Spaces written by Calvin C. Moore and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem [ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families [AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory.
Introduction To Global Variational Geometry
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Introduction To Global Variational Geometry written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces