On the Number of Simply Connected Minimal Surfaces Spanning a Curve.

Intro -- Table of Contents -- 0. Introduction -- I. A review of the Euler characteristic of a Palais-Smale vector field -- II. Analytical preliminaries - the Sobelev spaces -- III. The global formulation of the problem of Plateau -- IV. The existence of a vector field associated to the Dirichlet functional E[sub(α)] -- V. A proof that the vector field X[sup(α)], associated to E[sub(α)], is Palais-Smale -- VI. The weak Riemannian structure on η[sub(α)] -- VII. The equivariance of X[sup(α)] under the action of the conformal group -- VIII.The regularity results for minimal surfaces -- IX. The Fréchet derivative of the minimal surface vector field X and the surface fibre bundle -- X. The minimal surface vector field X is proper on bounded sets -- XI. Non-degenerate critical submanifolds of η[sub(α)] and a uniqueness theorem for minimal surfaces -- XII. The spray of the weak metric -- XIII. The transversality theorem -- XIV. The Morse number of minimal surfaces spanning a simple closed curve and its invarience under isotopy -- XV. References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.