eBook ISBN:  9781470400552 
Product Code:  MEMO/100/478.E 
List Price:  $29.00 
MAA Member Price:  $26.10 
AMS Member Price:  $17.40 
eBook ISBN:  9781470400552 
Product Code:  MEMO/100/478.E 
List Price:  $29.00 
MAA Member Price:  $26.10 
AMS Member Price:  $17.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 100; 1992; 77 ppMSC: 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 oneparameter families of immersed cmc tori in \(R^3\). Finally, Wente examines minimal surfaces in hyperbolic threespace, which is in some ways the most complicated case.
ReadershipDifferential 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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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 oneparameter families of immersed cmc tori in \(R^3\). Finally, Wente examines minimal surfaces in hyperbolic threespace, which is in some ways the most complicated case.
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