|Title||The Plateau Problem|
|Publisher||Gordon and Breach Science Publishers|
|Year of publication||1990|
|Reviewed by||Daniel Vacaretu|
Professor A.T. Fomenko, from the Faculty of Mechanics and Mathematics, Moscow State University, is a well-known specialist in the fields of geometry, topology and multidimensional variational calculus. He is, also, an expert in the famous Plateau problem. He published in 199O a valuable monograph: Variational; Principles of Topology (Kluwer Academic Publishers) which leading subject is the study of some multidimensional variational probleos, among them being the Plateau problem.
This new monograph has two parts.
In the first one, Historical Survey, the author discusses substantial extracts from 18th, 19th and early 20th century works devoted to the investigation of minimal surfaces, including Plateau's famous physical problem. The theories of homology and cohomology, necessary for an understanding of modern multidimensional, variational problems, are elucidated.
In the second part, The Present State of the Theory, the author demonstrates the deep rooted connections between the theory of minimal surfaces and modern branches of mathematics, particularly the theory of differential equations, Lie groups and multidimensional variational calculus.
The book is designed for mathematicians, specialists in calculus of variations, topology, functional analysis,theory of differential equations, and Lie groups and algebras.
These two parts represent a good investment for specialists and libraries.