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On the Number of Simply Connected Minimal Surfaces Spanning a Curve

eBook ISBN: | 978-1-4704-0155-9 |
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: | 978-1-4704-0155-9 |
Product Code: | MEMO/12/194.E |
List Price: | $25.00 |
MAA Member Price: | $22.50 |
AMS Member Price: | $20.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 12; 1977; 121 ppMSC: Primary 53; Secondary 58; 65
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Table of Contents
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Chapters
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I. A review of the Euler characteristic of a Palais-Smale vector field
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II. Analytical preliminaries – the Sobelev spaces
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III. The global formulation of the problem of Plateau
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IV. The existence of a vector field associated to the Dirichlet functional $E_\alpha $
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V. A proof that the vector field $X^\alpha $, associated to $E_\alpha $, is Palais-Smale
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VI. The weak Riemannian structure on $\mathcal {N}_\alpha $
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VII. The equivariance of $X^\alpha $ under the action of the conformal group
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VIII. The regularity results for minimal surfaces
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IX. The Fréchet derivative of the minimal surface vector field $X$ and the surface fibre bundle
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X. The minimal surface vector field $X$ is proper on bounded sets
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XI. Non-degenerate critical submanifolds of $\mathcal {N}_\alpha $ and a uniqueness theorem for minimal surfaces
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XII. The spray of the weak metric
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XIII. The transversality theorem
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XIV. The Morse number of minimal surfaces spanning a simple closed curve and its invariance under isotopy
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- 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 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_\alpha $
-
V. A proof that the vector field $X^\alpha $, associated to $E_\alpha $, is Palais-Smale
-
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. Non-degenerate 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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