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Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem (Translations of Mathematical Monographs) by Dao Trong Thi and A. T. Fomenko is a book available to read on EtoBox.

What is Minimal Surfaces, Stratified Multivarifolds, and the Plateau Problem (Translations of Mathematical Monographs) about?

<p>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 d

Author

Dao Trong Thi and A. T. Fomenko

Publisher

Providence, R.I.: American Mathematical Society

Published

2018

Language

EN

ISBN

9780821845363

Subjects

Mathematics, Stem