minimal surfaces stratified multivarifolds and the plateau problem translations of mathematical monographs

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Minimal Surfaces Stratified Multivarifolds And The Plateau Problem

Author : A. T. Fomenko
ISBN : 0821898272
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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.

Conformal Mappings And Boundary Value Problems

Author : Guo-Chun Wen
ISBN : 0821886800
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Tube Domains And The Cauchy Problem

Author : Semen Grigorʹevich Gindikin
ISBN : 0821897403
Genre : Mathematics
File Size : 27. 54 MB
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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

Author : Gennadij M. Fel'dman
ISBN : 0821845934
Genre : Mathematics
File Size : 37. 95 MB
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This book studies the problem of the decomposition of a given random variable into a sum of independent random variables (components). Starting from the famous Cramer theorem, which says that all components of a normal random variable are also normal random variables, the central feature of the book is Feldman's use of powerful analytical techniques. In the algebraic case, one cannot directly use analytic methods because of the absence of a natural analytic structure on the dual group, which is the domain of characteristic functions. Nevertheless, the methods developed in this book allow one to apply analytic techniques in the algebraic setting. The first part of the book presents results on the arithmetic of probability distributions of random variables with values in a locally compact abelian group. The second part studies problems of characterization of a Gaussian distribution of a locally compact abelian group by the independence or identical distribution of its linear statistics.

Russian Mathematical Surveys

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ISBN : UOM:39015039029957
Genre : Mathematics
File Size : 59. 57 MB
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Vietnam Journal Of Mathematics

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ISBN : UOM:39015055727948
Genre : Mathematics
File Size : 27. 18 MB
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Notices Of The American Mathematical Society

Author : American Mathematical Society
ISBN : UCSD:31822002324598
Genre : Mathematics
File Size : 64. 93 MB
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Mathematical Reviews

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ISBN : UOM:39015026169683
Genre : Mathematics
File Size : 51. 98 MB
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Cumulative Book Index

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ISBN : UOM:39015058373807
Genre : American literature
File Size : 66. 19 MB
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American Book Publishing Record

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ISBN : UOM:39015016314786
Genre : United States
File Size : 33. 85 MB
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