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On the Number of Simply Connected Minimal Surfaces Spanning a Curve
eBook ISBN:  9781470401559 
Product Code:  MEMO/12/194.E 
List Price:  $25.00 
MAA Member Price:  $22.50 
AMS Member Price:  $20.00 
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On the Number of Simply Connected Minimal Surfaces Spanning a Curve
eBook ISBN:  9781470401559 
Product Code:  MEMO/12/194.E 
List Price:  $25.00 
MAA Member Price:  $22.50 
AMS Member Price:  $20.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 12; 1977; 121 ppMSC: Primary 53; Secondary 58; 65

Table of Contents

Chapters

I. A review of the Euler characteristic of a PalaisSmale 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_\alpha $

V. A proof that the vector field $X^\alpha $, associated to $E_\alpha $, is PalaisSmale

VI. The weak Riemannian structure on $\mathcal {N}_\alpha $

VII. The equivariance of $X^\alpha $ 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. Nondegenerate critical submanifolds of $\mathcal {N}_\alpha $ 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 invariance under isotopy


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 Table of Contents
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Volume: 12; 1977; 121 pp
MSC: Primary 53; Secondary 58; 65

Chapters

I. A review of the Euler characteristic of a PalaisSmale 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_\alpha $

V. A proof that the vector field $X^\alpha $, associated to $E_\alpha $, is PalaisSmale

VI. The weak Riemannian structure on $\mathcal {N}_\alpha $

VII. The equivariance of $X^\alpha $ 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. Nondegenerate critical submanifolds of $\mathcal {N}_\alpha $ 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 invariance under isotopy
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