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Surfaces with Constant Mean Curvature

By: Katsuei Kenmotsu

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Paperback | 1 January 2003

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The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. There is a rich and well-known theory of minimal surfaces. A surface whose mean curvature is constant but nonzero is obtained when we try to minimize the area of a closed surface without changing the volume it encloses. An easy example of a surface of constant mean curvature is the sphere. A nontrivial example is provided by the constant curvature torus, whose discovery in 1984 gave a powerful incentive for studying such surfaces. Later, many examples of constant mean curvature surfaces were discovered using various methods of analysis, differential geometry, and differential equations. It is now becoming clear that there is a rich theory of surfaces of constant mean curvature. In this book, the author presents numerous examples of constant mean curvature surfaces and techniques for studying them. Many finely rendered figures illustrate the results and allow the reader to visualize and better understand these beautiful objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.

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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry

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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry

Other titles in this series
Preliminaries from the theory of surfaces
Mean curvature
Rotational surfaces
Helicoidal surfaces
Stability Tori
The balancing formula
The Gauss map
Intricate constant mean curvature surfaces
Supplement Programs for the figures Postscript
Bibliography
List of sources for the figures
Index
Table of Contents provided by Publisher. All Rights Reserved.

Surfaces with Constant Mean Curvature

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