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Author: Michael Struwe
Publisher: Princeton University Press
ISBN: 1400860210
Category : Mathematics
Languages : en
Pages : 159
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Book Description
This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail. The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Michael Struwe
Publisher: Princeton University Press
ISBN: 1400860210
Category : Mathematics
Languages : en
Pages : 159
Get Book
Book Description
This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail. The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: A. T. Fomenko
Publisher: American Mathematical Soc.
ISBN: 9780821898277
Category : Mathematics
Languages : en
Pages : 424
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Book Description
Plateau's problem is a scientific trend in modern mathematics that unites several different problems connected with the study of minimal surfaces. In its simplest version, Plateau's problem is concerned with finding a surface of least area that spans a given fixed one-dimensional contour in three-dimensional space--perhaps the best-known example of such surfaces is provided by soap films. From the mathematical point of view, such films are described as solutions of a second-order partial differential equation, so their behavior is quite complicated and has still not been thoroughly studied. Soap films, or, more generally, interfaces between physical media in equilibrium, arise in many applied problems in chemistry, physics, and also in nature. In applications, one finds not only two-dimensional but also multidimensional minimal surfaces that span fixed closed ``contours'' in some multidimensional Riemannian space. An exact mathematical statement of the problem of finding a surface of least area or volume requires the formulation of definitions of such fundamental concepts as a surface, its boundary, minimality of a surface, and so on. It turns out that there are several natural definitions of these concepts, which permit the study of minimal surfaces by different, and complementary, methods. In the framework of this comparatively small book it would be almost impossible to cover all aspects of the modern problem of Plateau, to which a vast literature has been devoted. However, this book makes a unique contribution to this literature, for the authors' guiding principle was to present the material with a maximum of clarity and a minimum of formalization. Chapter 1 contains historical background on Plateau's problem, referring to the period preceding the 1930s, and a description of its connections with the natural sciences. This part is intended for a very wide circle of readers and is accessible, for example, to first-year graduate students. The next part of the book, comprising Chapters 2-5, gives a fairly complete survey of various modern trends in Plateau's problem. This section is accessible to second- and third-year students specializing in physics and mathematics. The remaining chapters present a detailed exposition of one of these trends (the homotopic version of Plateau's problem in terms of stratified multivarifolds) and the Plateau problem in homogeneous symplectic spaces. This last part is intended for specialists interested in the modern theory of minimal surfaces and can be used for special courses; a command of the concepts of functional analysis is assumed.
Author: Themistocles M. Rassias
Publisher: World Scientific
ISBN: 9789810205560
Category : Mathematics
Languages : en
Pages : 350
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Book Description
This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rad¢. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.
Author: Tibor Radó
Publisher: Springer
ISBN: 3642991181
Category : Mathematics
Languages : en
Pages : 114
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Book Description
The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters.
Author: Frederick J. Almgren
Publisher: American Mathematical Soc.
ISBN: 0821827472
Category : Differential topology
Languages : en
Pages : 96
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Book Description
There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book - or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films.When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.
Author: Thomas Stützle
Publisher: Springer
ISBN: 3642037518
Category : Computers
Languages : en
Pages : 155
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Book Description
Stochastic local search (SLS) algorithms are established tools for the solution of computationally hard problems arising in computer science, business adm- istration, engineering, biology, and various other disciplines. To a large extent, their success is due to their conceptual simplicity, broad applicability and high performance for many important problems studied in academia and enco- tered in real-world applications. SLS methods include a wide spectrum of te- niques, ranging from constructive search procedures and iterative improvement algorithms to more complex SLS methods, such as ant colony optimization, evolutionary computation, iterated local search, memetic algorithms, simulated annealing, tabu search, and variable neighborhood search. Historically, the development of e?ective SLS algorithms has been guided to a large extent by experience and intuition. In recent years, it has become - creasingly evident that success with SLS algorithms depends not merely on the adoption and e?cient implementation of the most appropriate SLS technique for a given problem, but also on the mastery of a more complex algorithm - gineering process. Challenges in SLS algorithm development arise partly from the complexity of the problems being tackled and in part from the many - grees of freedom researchers and practitioners encounter when developing SLS algorithms. Crucial aspects in the SLS algorithm development comprise al- rithm design, empirical analysis techniques, problem-speci?c background, and background knowledge in several key disciplines and areas, including computer science, operations research, arti?cial intelligence, and statistics.
Author: Eugene W. Holland
Publisher: A&C Black
ISBN: 144116250X
Category : Philosophy
Languages : en
Pages : 191
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Book Description
A Thousand Plateaus is the engaging and influential second part of Capitalism and Schizophrenia, the remarkable collaborative project written by the philosopher Gilles Deleuze and the psychoanalyst Félix Guattari. This hugely important text is a work of staggering complexity that made a major contribution to contemporary Continental philosophy, yet remains distinctly challenging for readers in a number of disciplines. Deleuze and Guattari's 'A Thousand Plateaus': A Reader's Guide offers a concise and accessible introduction to this extremely important and yet challenging work. Written specifically to meet the needs of students coming to Deleuze and Guattari for the first time, the book offers guidance on: - Philosophical and historical context - Key themes - Reading the text - Reception and influence - Further reading
Author: Brent Adkins
Publisher: Edinburgh University Press
ISBN: 0748686479
Category : Philosophy
Languages : en
Pages : 272
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Book Description
Using clear language and numerous examples, each chapter of this guide analyses an individual plateau from Deleuze and Guattari's A Thousand Plateaus, interpreting the work for students and scholars.
Author: Günter Rudolph
Publisher: Springer
ISBN: 3540877002
Category : Computers
Languages : en
Pages : 1183
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Book Description
This book constitutes the refereed proceedings of the 10th International Conference on Parallel Problem Solving from Nature, PPSN 2008, held in Dortmund, Germany, in September 2008. The 114 revised full papers presented were carefully reviewed and selected from 206 submissions. The conference covers a wide range of topics, such as evolutionary computation, quantum computation, molecular computation, neural computation, artificial life, swarm intelligence, artificial ant systems, artificial immune systems, self-organizing systems, emergent behaviors, and applications to real-world problems. The paper are organized in topical sections on formal theory, new techniques, experimental analysis, multiobjective optimization, hybrid methods, and applications.
Author: Library of Congress. Cataloging Policy and Support Office
Publisher:
ISBN:
Category : Subject headings, Library of Congress
Languages : en
Pages : 1172
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Book Description
