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Some Nonlinear Problems in Riemannian Geometry

Some Nonlinear Problems in Riemannian Geometry Author Thierry Aubin
ISBN-10 9783662130063
Release 2013-03-09
Pages 398
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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.

Some Nonlinear Problems in Riemannian Geometry

Some Nonlinear Problems in Riemannian Geometry Author Thierry Aubin
ISBN-10 3540607528
Release 1998-06-22
Pages 398
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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.

Some Nonlinear Problems in Riemannian Geometry

Some Nonlinear Problems in Riemannian Geometry Author Thierry Aubin
ISBN-10 3662130076
Release 2014-01-15
Pages 420
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Some Nonlinear Problems in Riemannian Geometry has been writing in one form or another for most of life. You can find so many inspiration from Some Nonlinear Problems in Riemannian Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Some Nonlinear Problems in Riemannian Geometry book for free.

Methods in Nonlinear Analysis

Methods in Nonlinear Analysis Author Kung Ching Chang
ISBN-10 9783540292326
Release 2006-03-30
Pages 442
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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.

Nonlinear Analysis on Manifolds Monge Amp re Equations

Nonlinear Analysis on Manifolds  Monge Amp  re Equations Author T. Aubin
ISBN-10 9781461257349
Release 2012-12-06
Pages 204
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This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.

Riemannian Geometry and Geometric Analysis

Riemannian Geometry and Geometric Analysis Author Jürgen Jost
ISBN-10 9783319618609
Release 2017-10-13
Pages 697
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This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik

Spherical Inversion on SLn R

Spherical Inversion on SLn R Author Jay Jorgenson
ISBN-10 9781468493023
Release 2012-12-06
Pages 426
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For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.

Solitons in Field Theory and Nonlinear Analysis

Solitons in Field Theory and Nonlinear Analysis Author Yisong Yang
ISBN-10 9781475765489
Release 2013-03-14
Pages 553
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There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

Fractal Geometry Complex Dimensions and Zeta Functions

Fractal Geometry  Complex Dimensions and Zeta Functions Author Michel Lapidus
ISBN-10 9781461421757
Release 2012-09-20
Pages 570
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Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.

Nonlinear PDEs

Nonlinear PDEs Author Marius Ghergu
ISBN-10 9783642226649
Release 2011-10-22
Pages 394
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The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.​

Nonlinear Analysis on Manifolds

Nonlinear Analysis on Manifolds Author Emmanuel Hebey
ISBN-10 9780821827000
Release 2000-10-27
Pages 290
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This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. ``Several surprising phenomena appear when studying Sobolev spaces on manifolds,'' according to the author. ``Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.'' The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.

Applications of Contact Geometry and Topology in Physics

Applications of Contact Geometry and Topology in Physics Author Arkady Leonidovich Kholodenko
ISBN-10 9789814412094
Release 2013
Pages 492
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Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Certified Reduced Basis Methods for Parametrized Partial Differential Equations Author Jan S Hesthaven
ISBN-10 9783319224701
Release 2015-08-20
Pages 131
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This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Understanding Nonlinear Dynamics

Understanding Nonlinear Dynamics Author Daniel Kaplan
ISBN-10 9781461208235
Release 2012-12-06
Pages 420
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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics ( TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.

The Ricci Flow in Riemannian Geometry

The Ricci Flow in Riemannian Geometry Author Ben Andrews
ISBN-10 9783642162855
Release 2010-11-25
Pages 296
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Focusing on Hamilton's Ricci flow, this volume begins with a detailed discussion of the required aspects of differential geometry. The discussion also includes existence and regularity theory, compactness theorems for Riemannian manifolds, and much more.

Concrete Functional Calculus

Concrete Functional Calculus Author R. M. Dudley
ISBN-10 1441969500
Release 2010-11-03
Pages 671
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Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are proved under suitable assumptions for nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation. Key features and topics: Extensive usage of p-variation of functions, and applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.

40 Days of Dating

40 Days of Dating Author Jessica Walsh
ISBN-10 9781613127155
Release 2015-01-20
Pages 304
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When New York–based graphic designers and long-time friends Timothy Goodman and Jessica Walsh found themselves single at the same time, they decided to try an experiment. The old adage says that it takes 40 days to change a habit—could the same be said for love? So they agreed to date each other for 40 days, record their experiences in questionnaires, photographs, videos, texts, and artworks, and post the material on a website they would create for this purpose. What began as a small experiment between two friends became an Internet sensation, drawing 5 million unique (and obsessed) visitors from around the globe to their site and their story since it was launched in July 2013. 40 Days of Dating: An Experiment is a beautifully designed, expanded look at the experiment and the results, including a great deal of material that never made it onto the site, such as who they were as friends and individuals before the 40 days and who they have become since. Note: 40 Days of Dating has a special binding that allows it to open very flat by attaching the endpapers to the inside covers.