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Constant Mean Curvature Immersions of Enneper Type
 
Constant Mean Curvature Immersions of Enneper Type
eBook 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
Constant Mean Curvature Immersions of Enneper Type
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Constant Mean Curvature Immersions of Enneper Type
eBook 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
  • Requests
     
     
    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
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
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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