Author : Anonim
Publisher : Unknown
Page : 404 pages
File Size : 55,6 Mb
Release : 1962
Category : Mathematics
ISBN : 0821845365
Translations of Mathematical Monographs
Anonim
Minimal Surfaces Stratified Multivarifolds And The Plateau Problem
Minimal Surfaces Stratified Multivarifolds And The Plateau Problem Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Minimal Surfaces Stratified Multivarifolds And The Plateau Problem book. This book definitely worth reading, it is an incredibly well-written.
Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem
A. T. Fomenko
Author : A. T. Fomenko
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 42,6 Mb
Release : 1991-02-21
Category : Mathematics
ISBN : 0821898272
Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem by A. T. Fomenko Pdf
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.
A Survey of Minimal Surfaces
Robert Osserman
Author : Robert Osserman
Publisher : Courier Corporation
Page : 226 pages
File Size : 54,9 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 9780486649986
A Survey of Minimal Surfaces by Robert Osserman Pdf
This clear and comprehensive study features 12 sections that discuss parametric and non-parametric surfaces, surfaces that minimize area, isothermal parameters, Bernstein's theorem, minimal surfaces with boundary, and many other topics. This revised edition includes material on minimal surfaces in relativity and topology and updated work on Plateau's problem and isoperimetric inequalities. 1969 edition.
Plateau's Problem and the Calculus of Variations. (MN-35)
Michael Struwe
Author : Michael Struwe
Publisher : Princeton University Press
Page : 159 pages
File Size : 42,9 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400860210
Plateau's Problem and the Calculus of Variations. (MN-35) by Michael Struwe Pdf
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.
The Problem of Plateau
Themistocles M. Rassias
Author : Themistocles M. Rassias
Publisher : World Scientific
Page : 350 pages
File Size : 50,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9810205562
The Problem of Plateau by Themistocles M. Rassias Pdf
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.
Minimal Surfaces
A. T. Fomenko
Author : A. T. Fomenko
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 50,9 Mb
Release : 1993
Category : Minimal surfaces
ISBN : 0821841165
Minimal Surfaces by A. T. Fomenko Pdf
This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.
Minimal Surfaces and Functions of Bounded Variation
Giusti
Author : Giusti
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 53,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781468494860
Minimal Surfaces and Functions of Bounded Variation by Giusti Pdf
The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Problems and Theorems in Linear Algebra
Viktor Vasil_evich Prasolov
Author : Viktor Vasil_evich Prasolov
Publisher : American Mathematical Soc.
Page : 225 pages
File Size : 46,9 Mb
Release : 1994-06-13
Category : Mathematics
ISBN : 9780821802366
Problems and Theorems in Linear Algebra by Viktor Vasil_evich Prasolov Pdf
There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.
Conformal Mappings and Boundary Value Problems
Guo-Chun Wen
Author : Guo-Chun Wen
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 43,8 Mb
Release : 2024-06-06
Category : Mathematics
ISBN : 0821886800
Conformal Mappings and Boundary Value Problems by Guo-Chun Wen Pdf
Translated from the Chinese. Conformal mapping and boundary value problems are two major branches of complex function theory. The former is the geometric theory of analytic functions, and the latter is the analysis theory governing the close relationship between abstract theory and many concrete problems. Topics include applications of Cauchy type integrals, the Hilbert boundary value problem, quasiconformal mappings, and basic boundary value problems for harmonic functions. Annotation copyright by Book News, Inc., Portland, OR
Tube Domains and the Cauchy Problem
Semen Grigorʹevich Gindikin
Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 42,7 Mb
Release : 2024-06-06
Category : Mathematics
ISBN : 0821897403
Tube Domains and the Cauchy Problem by Semen Grigorʹevich Gindikin Pdf
This book is dedicated to two problems. The first concerns the description of maximal exponential growth of functions or distributions for which the Cauchy problem is well posed. The descriptions presented in the language of the behaviour of the symbol in a complex domain. The second problem concerns the structure of and explicit formulas for differential operators with large automorphism groups. It is suitable as an advanced graduate text in courses in partial differential equations and the theory of distributions.
Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups
Gennadiĭ Mikhaĭlovich Felʹdman
Author : Gennadiĭ Mikhaĭlovich Felʹdman
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 41,8 Mb
Release : 1993
Category : Mathematics
ISBN : 0821845934
Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups by Gennadiĭ Mikhaĭlovich Felʹdman Pdf
This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups
Gennadij M. Fel'dman
Author : Gennadij M. Fel'dman
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 50,7 Mb
Release : 2024-06-06
Category : Mathematics
ISBN : 0821897446
Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups by Gennadij M. Fel'dman Pdf
This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Selected Problems in Real Analysis
M. G. Goluzina,A. A. Lodkin,A. N. Podkorytov
Author : M. G. Goluzina,A. A. Lodkin,A. N. Podkorytov
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 54,7 Mb
Release : 2024-06-06
Category : Mathematics
ISBN : 0821897381
Selected Problems in Real Analysis by M. G. Goluzina,A. A. Lodkin,A. N. Podkorytov Pdf
This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore.
Variational Problems in Topology
A.T. Fomenko
Author : A.T. Fomenko
Publisher : Routledge
Page : 226 pages
File Size : 46,6 Mb
Release : 2019-06-21
Category : Mathematics
ISBN : 9781351405683
Variational Problems in Topology by A.T. Fomenko Pdf
Many of the modern variational problems of topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics. In this work, Professor Fomenko offers a concise and clear explanation of some of these problems (both solved and unsolved), using current methods of analytical topology. His book falls into three interrelated sections. The first gives an elementary introduction to some of the most important concepts of topology used in modern physics and mechanics: homology and cohomology, and fibration. The second investigates the significant role of Morse theory in modern aspects of the topology of smooth manifolds, particularly those of three and four dimensions. The third discusses minimal surfaces and harmonic mappings, and presents a number of classic physical experiments that lie at the foundations of modern understanding of multidimensional variational calculus. The author's skilful exposition of these topics and his own graphic illustrations give an unusual motivation to the theory expounded, and his work is recommended reading for specialists and non-specialists alike, involved in the fields of physics and mathematics at both undergraduate and graduate levels.
Minimal Surfaces
Tobias H. Colding,William P. Minicozzi
Author : Tobias H. Colding,William P. Minicozzi
Publisher : Courant Institute of Mathemetical Sciences
Page : 136 pages
File Size : 55,9 Mb
Release : 1999
Category : Mathematics
ISBN : STANFORD:36105021943365