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Author: Vladimir M. Manuilov Publisher: Springer Nature ISBN: 3030373266 Category : Mathematics Languages : en Pages : 349
Book Description
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.
Author: Vladimir M. Manuilov Publisher: Springer Nature ISBN: 3030373266 Category : Mathematics Languages : en Pages : 349
Book Description
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.
Author: Gerardo F. Torres del Castillo Publisher: Springer Science & Business Media ISBN: 0817682716 Category : Mathematics Languages : en Pages : 280
Book Description
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.
Author: Shing-Tung Yau Publisher: Princeton University Press ISBN: 0691082960 Category : Mathematics Languages : en Pages : 720
Book Description
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.
Author: Keti Tenenblat Publisher: Chapman & Hall/CRC ISBN: Category : Mathematics Languages : en Pages : 232
Book Description
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.
Author: Yuri E. Gliklikh Publisher: Springer Science & Business Media ISBN: 9401586349 Category : Mathematics Languages : en Pages : 207
Book Description
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.
Author: James Kirkwood Publisher: Academic Press ISBN: 0123869110 Category : Mathematics Languages : en Pages : 431
Book Description
Suitable for advanced undergraduate and beginning graduate students taking a course on mathematical physics, this title presents some of the most important topics and methods of mathematical physics. It contains mathematical derivations and solutions - reinforcing the material through repetition of both the equations and the techniques.
Author: Jrgen Eichhorn Publisher: World Scientific ISBN: 981277145X Category : Mathematics Languages : en Pages : 353
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: Alexander Grigor'yan Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110700859 Category : Mathematics Languages : en Pages : 337
Book Description
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.
Author: Vladimir M. Manuilov
Author: Vladimir M. Manuilov
Author: Gerardo F. Torres del Castillo
Author: Shing-Tung Yau
Author: 
Author: Keti Tenenblat
Author: Yuri E. Gliklikh
Author: 
Author: James Kirkwood
Author: Jrgen Eichhorn
Author: Alexander Grigor'yan