Download or read book Differential Equations on Manifolds and Mathematical Physics written by Vladimir M. Manuilov and published by Springer Nature. This book was released on 2022-01-21 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume originating from the Conference on Partial Differential Equations and Applications, which was held in Moscow in November 2018 in memory of professor Boris Sternin and attracted more than a hundred participants from eighteen countries. The conference was mainly dedicated to partial differential equations on manifolds and their applications in mathematical physics, geometry, topology, and complex analysis. The volume contains selected contributions by leading experts in these fields and presents the current state of the art in several areas of PDE. It will be of interest to researchers and graduate students specializing in partial differential equations, mathematical physics, topology, geometry, and their applications. The readers will benefit from the interplay between these various areas of mathematics.

Download or read book Differentiable Manifolds written by Gerardo F. Torres del Castillo and published by Springer Science & Business Media. This book was released on 2011-10-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics.

Download or read book Seminar on Differential Geometry written by Shing-Tung Yau and published by Princeton University Press. This book was released on 1982-03-21 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.

Download or read book Differential Manifolds and Theoretical Physics written by and published by Academic Press. This book was released on 1985-05-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Manifolds and Theoretical Physics

Download or read book Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics written by Yuri E. Gliklikh and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

Download or read book Transformations of Manifolds and Applications to Differential Equations written by Keti Tenenblat and published by Chapman & Hall/CRC. This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between differential geometry and partial differential equations has been studied since the last century. This relationship is based on the fact that most of the local properties of manifolds are expressed in terms of partial differential equations. The correspondence between certain classes of manifolds and the associated differential equations can be useful in two ways. From our knowledge about the geometry of the manifolds we can obtain solutions to the equations. In particular it is important to study transformations of manifolds which preserve a geometric property, since the analytic interpretation of these transformations will provide mappings between the corresponding differential equations. Conversely, we can obtain geometric properties of the manifolds or even prove the non existence of certain geometric structures on manifolds from our knowledge of the differential equation. This kind of interaction between differential geometry and differential equations is the general theme of the book. The author focuses on the role played by differential geometry in the study of differential equations, combining the geometric and analytic aspects of the theory, not only in the classical examples but also in results obtained since 1980, on integrable systems with an arbitrary number of independent variables. The book will be of interest to graduate students, researchers and mathematicians working in differential geometry, differential equations and mathematical physics.

Download or read book Pseudo Differential Operators on Manifolds with Singularities written by B.-W. Schulze and published by Elsevier. This book was released on 1991-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics.The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.

Download or read book Differential Geometry Geometry in Mathematical Physics and Related Topics written by Robert Everist Greene and published by American Mathematical Soc.. This book was released on 1993 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

Download or read book The Geometry of Walker Manifolds written by Peter Gilkey and published by Springer Nature. This book was released on 2022-05-31 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications : Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds

Download or read book Differential Equations Asymptotic Analysis and Mathematical Physics written by Michael Demuth and published by John Wiley & Sons. This book was released on 1997 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.

Download or read book Analysis and Partial Differential Equations on Manifolds Fractals and Graphs written by Alexander Grigor'yan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.

Download or read book Partial Differential Equations III written by Michael E. Taylor and published by Springer Nature. This book was released on 2023-12-06 with total page 774 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^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. 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)

Download or read book Dynamical Systems and Geometric Mechanics written by Jared Maruskin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-21 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

Download or read book Differential Geometric Methods in Mathematical Physics written by S. Sternberg and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following pages represent the Proceedings of the XI Annual Conference on Differential Geometric Methods in Mathematical Physics which was held in Jerusalem from August 5 through 11, 1982 under the auspices of the Tel Aviv University and the Israel Academy of Sciences and Humanities. In addition to the above mentioned institutions, partial financial support was received form the Bank Leumi Lelsrael Fund for International Conferences, the American Friends of the Tel Aviv Institute of Mathematical Sciences and the Mathematics and Physics Branch of the United States Army Research, Development and Standardization Group (UK). We are grateful to all of these organizations for their financial support. GAUGE THEORY AND NUCLEAR STRUCTURE K. Bleuler Institut fur Theoretische Kernphysik der Universitat Bonn NuBallee 14-16, D-5300 Bonn, West-Germany I. INTRODUCTION The recent, most impressive verification of the Salam­ -Weinberg theory of electro-weak interactions through the experimental discovery of the so-called inter­ mediate bosons represents, at the same time, a success of the general gauge theoretical viewpoints in modern particle physics (quantum chromodynamics, 0CD). This theory leads to a deeper and by far more natural inter­ pretation of particle interaction and induces, as we shall see, also a profound change in our understanding of nuclear structure.

Download or read book Differential Geometry Partial differential equations on manifolds written by Robert Everist Greene and published by Amer Mathematical Society. This book was released on 1993 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Mechanics on Riemannian Manifolds written by Ovidiu Calin and published by Springer Science & Business Media. This book was released on 2006-03-15 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: * A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Download or read book Differential Forms with Applications to the Physical Sciences written by Harley Flanders and published by Courier Corporation. This book was released on 2012-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: "To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." — T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.