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- W609517869 abstract "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. Part 4 Modern state of minimal surface theory: minimal surfaces and homology integral currents minimal currents in Riemannian manifolds minimization of volumes of manifolds with fixed boundary and of closed manifolds - existence of a minimum in each spectral bordism class generalized homology and cohomology theories and their relation to the multidimensional Plateau problem existence of a minimum in each homotopy class of multivarifolds cases where a solution of the Dirichlet problem for the equation of minimal surfaces of high codimensions does not exist example of a smooth, closed, unknotted, curve in R3 bounding only minimal surfaces of large genus certain new methods of effective construction of globally minimal surfaces in Riemannian manifolds totally geodesic surfaces realizing non-trivial cycles, cocycles, and elements of homotopy groups in symmetric spaces Bott periodicity and its relation with the multidimensional Dirichlet functional survey of some recent results in harmonic mapping theory." @default.
- W609517869 created "2016-06-24" @default.
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- W609517869 date "1990-01-01" @default.
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- W609517869 title "The present state of the theory" @default.
- W609517869 hasPublicationYear "1990" @default.
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