Charting the historical origins of thr Plateau problem, 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 experiments. The theories of homology and co-homology, necessary for an understanding of modern multi-dimensional variational problems, are elucidated.
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Verlagsort
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Höhe: 229 mm
Breite: 152 mm
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ISBN-13
978-2-88124-700-2 (9782881247002)
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Autor*in
Moscow State University, Russia
Part 1 Historical survey and introduction to the theory of minimal surfaces: the origins of multidimensional variational calculus; the nineteenth century, the era of the discovery of basic minimal surface properties; topological and physical properties of minimal surfaces; the Plateau principles - minimal surfaces in animate nature. Part 2 Survey of some important publications in minimal surface theory from the nineteenth to the early twentieth century: Monge (1746-1818); Poisson (1781-1840); Plateau (1801-1883); some works of the early twentieth century Rado, Douglan; minimal surfaces in the large. Part 3 Some facts from elementary topology: singular and cellular homology groups; cohomology groups and obstructions to the extensions of mappings.
