Nonlinear Methods In Rimannian And Kahlerian Geometry

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Nonlinear Methods in Riemannian and Kählerian Geometry

Author : J. Jost
Publisher : Birkhäuser
ISBN 13 : 3034876904
Total Pages : 153 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Nonlinear Methods in Riemannian and Kählerian Geometry by : J. Jost

Download or read book Nonlinear Methods in Riemannian and Kählerian Geometry written by J. Jost and published by Birkhäuser. This book was released on 2013-04-17 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Diisseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature leads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second order nonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more prominent role in geometry. Let us list some of the most important ones: - harmonic maps between Riemannian and Kahlerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on Kahler manifolds - Yang-Mills equations in vector bundles over manifolds. While the solution of these equations usually is nontrivial, it can lead to very signifi cant results in geometry, as solutions provide maps, submanifolds, metrics, or connections which are distinguished by geometric properties in a given context. All these equations are elliptic, but often parabolic equations are used as an auxiliary tool to solve the elliptic ones.

Nonlinear Methods in Riemannian and Kählerian Geometry

Author : Jürgen Jost
Publisher : Birkhauser
ISBN 13 : 9780817626853
Total Pages : 154 pages
Book Rating : 4.6/5 (268 download)

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Book Synopsis Nonlinear Methods in Riemannian and Kählerian Geometry by : Jürgen Jost

Download or read book Nonlinear Methods in Riemannian and Kählerian Geometry written by Jürgen Jost and published by Birkhauser. This book was released on 1991 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Methods in Riemannian and Kahlerian Geometry

Author : Jurgen Jost
Publisher :
ISBN 13 : 9783034877077
Total Pages : 160 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis Nonlinear Methods in Riemannian and Kahlerian Geometry by : Jurgen Jost

Download or read book Nonlinear Methods in Riemannian and Kahlerian Geometry written by Jurgen Jost and published by . This book was released on 2014-01-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Partial Differential Equations II

Author : Michael E. Taylor
Publisher : Springer Nature
ISBN 13 : 303133700X
Total Pages : 706 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Partial Differential Equations II by : Michael E. Taylor

Download or read book Partial Differential Equations II written by Michael E. Taylor and published by Springer Nature. This book was released on 2023-12-06 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)

Algebraic and Differential Methods for Nonlinear Control Theory

Author : Rafael Martínez-Guerra
Publisher : Springer
ISBN 13 : 3030120252
Total Pages : 196 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Algebraic and Differential Methods for Nonlinear Control Theory by : Rafael Martínez-Guerra

Download or read book Algebraic and Differential Methods for Nonlinear Control Theory written by Rafael Martínez-Guerra and published by Springer. This book was released on 2019-01-30 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter. This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra.

Partial Differential Equations III

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 1441970495
Total Pages : 734 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Partial Differential Equations III by : Michael E. Taylor

Download or read book Partial Differential Equations III written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis

Kikagakuteki Henbun Mondai

Author : Seiki Nishikawa
Publisher : American Mathematical Soc.
ISBN 13 : 9780821813560
Total Pages : 236 pages
Book Rating : 4.8/5 (135 download)

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Book Synopsis Kikagakuteki Henbun Mondai by : Seiki Nishikawa

Download or read book Kikagakuteki Henbun Mondai written by Seiki Nishikawa and published by American Mathematical Soc.. This book was released on 2002 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A minimal length curve joining two points in a surface is called a geodesic. One may trace the origin of the problem of finding geodesics back to the birth of calculus. Many contemporary mathematical problems, as in the case of geodesics, may be formulated as variational problems in surfaces or in a more generalized form on manifolds. One may characterize geometric variational problems as a field of mathematics that studies global aspects of variational problems relevant in the geometry and topology of manifolds. For example, the problem of finding a surface of minimal area spanning a given frame of wire originally appeared as a mathematical model for soap films. It has also been actively investigated as a geometric variational problem. With recent developments in computer graphics, totally new aspects of the study on the subject have begun to emerge. This book is intended to be an introduction to some of the fundamental questions and results in geometric variational problems, studying variational problems on the length of curves and the energy of maps. The first two chapters treat variational problems of the length and energy of curves in Riemannian manifolds, with an in-depth discussion of the existence and properties of geodesics viewed as solutions to variational problems. In addition, a special emphasis is placed on the facts that concepts of connection and covariant differentiation are naturally induced from the formula for the first variation in this problem, and that the notion of curvature is obtained from the formula for the second variation. The last two chapters treat the variational problem on the energy of maps between two Riemannian manifolds and its solution, harmonic maps. The concept of a harmonic map includes geodesics and minimal submanifolds as examples. Its existence and properties have successfully been applied to various problems in geometry and topology. The author discusses in detail the existence theorem of Eells-Sampson, which is considered to be the most fundamental among existence theorems for harmonic maps. The proof uses the inverse function theorem for Banach spaces. It is presented to be as self-contained as possible for easy reading. Each chapter may be read independently, with minimal preparation for covariant differentiation and curvature on manifolds. The first two chapters provide readers with basic knowledge of Riemannian manifolds. Prerequisites for reading this book include elementary facts in the theory of manifolds and functional analysis, which are included in the form of appendices. Exercises are given at the end of each chapter. This is the English translation of a book originally published in Japanese. It is an outgrowth of lectures delivered at Tohoku University and at the Summer Graduate Program held at the Institute for Mathematics and its Applications at the University of Minnesota. It would make a suitable textbook for advanced undergraduates and graduate students. This item will also be of interest to those working in analysis.

Partial Differential Equations II

Author : Michael Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 1475741871
Total Pages : 547 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Partial Differential Equations II by : Michael Taylor

Download or read book Partial Differential Equations II written by Michael Taylor and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centred about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion.

Complex Nonlinearity

Author : Vladimir G. Ivancevic
Publisher : Springer Science & Business Media
ISBN 13 : 3540793577
Total Pages : 855 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Complex Nonlinearity by : Vladimir G. Ivancevic

Download or read book Complex Nonlinearity written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2008-05-31 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.

Geometric Evolution Equations

Author : Shu-Cheng Chang
Publisher : American Mathematical Soc.
ISBN 13 : 9780821857014
Total Pages : 252 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Geometric Evolution Equations by : Shu-Cheng Chang

Download or read book Geometric Evolution Equations written by Shu-Cheng Chang and published by American Mathematical Soc.. This book was released on 2005-01-11 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds. The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincare Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas. Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci flow, function theory on Kahler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem. The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology. Related titles of interest include The Ricci Flow: An Introduction.

Nonlinear Analysis in Geometry and Applied Mathematics

Author : Lydia Bieri
Publisher :
ISBN 13 : 9781571463449
Total Pages : 157 pages
Book Rating : 4.4/5 (634 download)

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Book Synopsis Nonlinear Analysis in Geometry and Applied Mathematics by : Lydia Bieri

Download or read book Nonlinear Analysis in Geometry and Applied Mathematics written by Lydia Bieri and published by . This book was released on 2017 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the 2015-2016 year at Harvard University's Center of Mathematical Sciences and Applications (CMSA), several researchers working in mathematical general relativity presented lectures on modern topics of research in the field of "Non-linear Equations." This volume presents articles--by those researchers and their co-authors--drawn from their CMSA lectures. Specific topics include the Cauchy problem for the Einstein equations in cosmological and non-cosmological settings; investigation of stability as well as singularities (black holes) of classes of spacetimes; initial data engineering; gravitational radiation; and asymptotics of spacetimes, quasi-local energies, and their limits. The content of this volume reflects some of the activities at the Harvard CMSA during the 2015-2016 program, and provides insights into active areas of research in mathematical general relativity that can benefit scholars working in PDEs, geometric analysis, and general relativity.

Fundamental Groups of Compact Kahler Manifolds

Author : Jaume Amorós
Publisher : American Mathematical Soc.
ISBN 13 : 0821804987
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fundamental Groups of Compact Kahler Manifolds by : Jaume Amorós

Download or read book Fundamental Groups of Compact Kahler Manifolds written by Jaume Amorós and published by American Mathematical Soc.. This book was released on 1996 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kähler manifolds. Most of these results are negative ones, saying which groups don not arise. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.

Partial Differential Equations

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 9780387946542
Total Pages : 590 pages
Book Rating : 4.9/5 (465 download)

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Book Synopsis Partial Differential Equations by : Michael E. Taylor

Download or read book Partial Differential Equations written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 1996-06-25 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. Companion texts, which take the theory of partial differential equations further, are AMS volume 116, treating more advanced topics in linear PDE, and AMS volume 117, treating problems in nonlinear PDE. This book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

Some Nonlinear Problems in Riemannian Geometry

Author : Thierry Aubin
Publisher : Springer Science & Business Media
ISBN 13 : 3662130068
Total Pages : 414 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Some Nonlinear Problems in Riemannian Geometry by : Thierry Aubin

Download or read book Some Nonlinear Problems in Riemannian Geometry written by Thierry Aubin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.

Methods in Nonlinear Analysis

Author : Kung Ching Chang
Publisher : Springer
ISBN 13 : 9783540806257
Total Pages : 442 pages
Book Rating : 4.8/5 (62 download)

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Book Synopsis Methods in Nonlinear Analysis by : Kung Ching Chang

Download or read book Methods in Nonlinear Analysis written by Kung Ching Chang and published by Springer. This book was released on 2009-09-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.

Partial Differential Equations I

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 144197055X
Total Pages : 673 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Partial Differential Equations I by : Michael E. Taylor

Download or read book Partial Differential Equations I written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

Partial Differential Equations I

Author : Michael Eugene Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 9780387946535
Total Pages : 600 pages
Book Rating : 4.9/5 (465 download)

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Book Synopsis Partial Differential Equations I by : Michael Eugene Taylor

Download or read book Partial Differential Equations I written by Michael Eugene Taylor and published by Springer Science & Business Media. This book was released on 1996 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.