The work of Jesse Douglas on Minimal Surfaces
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s of papers published by Jesse DouglasAll references are to the Bulletin of the American Mathematical Society and takethe form year, page, article number. [4] (1927, 143-4, 32) Reduction of the problem of Plateau to an integral equation.[5] (1927, 259, 5) Reduction to integral equations of the problem of Plateau for the case of twocontours.[6] (1928, 405, 5) Reduction of the problem of Plateau to the minimization of a certain functional. THE WORK OF JESSE DOUGLAS ON MINIMAL SURFACES301
منابع مشابه
On the Existence of Minimal Surfaces with Singular Boundaries
In 1931, Jesse Douglas showed that in Rn, every set of k rectifiable Jordan curves, with k ≥ 2, bounds an area-minimizing minimal surface with prescribed topological type if a “condition of cohesion” is satisfied. In this paper, it is established that under similar conditions, this result can be extended to non-Jordan curves.
متن کاملDigital cohomology groups of certain minimal surfaces
In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...
متن کاملThe work of Jesse Douglas on Minimal Surface
The demonstration of the existence of a least-area surface spanning a given contour has a long history. Through the soap-film experiments of Plateau, this existence problem became known as the Plateau Problem. By the end of the 19th century, the list of contours for which the Plateau problem could be solved was intriguingly close to that considered by Plateau, namely polygonal contours, lines o...
متن کاملOn 5-dimensional 2-step homogeneous randers nilmanifolds of Douglas type
In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five. Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces. Moreover, we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...
متن کاملSecond Variation of Energy for Minimal Surfaces in Riemannian Manifolds
This article describes a formula for second variation of energy for twodimensional parametrized minimal surfaces, in which the conformal structure on the two-dimensional domain is allowed to vary. Moreover, it shows that minimal surfaces with branch points have tangential Jacobi fields which are not visible via the standard formulae for second variation of area which is commonly used to study s...
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تاریخ انتشار 2016