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Constant Mean Curvature Immersions of Enneper Type

Available Formats:
Electronic ISBN: 978-1-4704-0055-2
Product Code: MEMO/100/478.E
List Price: $29.00 MAA Member Price:$26.10
AMS Member Price: $17.40 Click above image for expanded view Constant Mean Curvature Immersions of Enneper Type Available Formats:  Electronic ISBN: 978-1-4704-0055-2 Product Code: MEMO/100/478.E  List Price:$29.00 MAA Member Price: $26.10 AMS Member Price:$17.40
• Book Details

Memoirs of the American Mathematical Society
Volume: 1001992; 77 pp
MSC: Primary 53;

This work is devoted to the case of constant mean curvature surfaces immersed in $R^3$ (or, more generally, in spaces of constant curvature). Wente reduces this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in $R^3$ with embedded Delaunay ends and $n$-lobes in the middle, and one-parameter families of immersed cmc tori in $R^3$. Finally, Wente examines minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.

Readership

Differential geometers interested in the theory of constant mean curvature surfaces and minimal surfaces. Experts in integrable systems of differential equations.

• Table of Contents

• Chapters
• I. Introduction
• II. The differential geometry
• III. $H = 1/2$ immersions in $\mathbf {R}^3$
• IV. Minimal surfaces in $\mathbf {R}^3$
• V. Minimal surfaces in $H^3$
• VI. Illustrations
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Volume: 1001992; 77 pp
MSC: Primary 53;

This work is devoted to the case of constant mean curvature surfaces immersed in $R^3$ (or, more generally, in spaces of constant curvature). Wente reduces this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in $R^3$ with embedded Delaunay ends and $n$-lobes in the middle, and one-parameter families of immersed cmc tori in $R^3$. Finally, Wente examines minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.

Readership

Differential geometers interested in the theory of constant mean curvature surfaces and minimal surfaces. Experts in integrable systems of differential equations.

• Chapters
• I. Introduction
• II. The differential geometry
• III. $H = 1/2$ immersions in $\mathbf {R}^3$
• IV. Minimal surfaces in $\mathbf {R}^3$
• V. Minimal surfaces in $H^3$
• VI. Illustrations
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