SoftcoverISBN:  9780821834794 
Product Code:  MMONO/221 
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eBookISBN:  9781470446451 
Product Code:  MMONO/221.E 
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AMS Member Price:  $53.60 
SoftcoverISBN:  9780821834794 
eBookISBN:  9781470446451 
Product Code:  MMONO/221.B 
List Price:  $139.00$105.50 
MAA Member Price:  $125.10$94.95 
AMS Member Price:  $111.20$84.40 
Softcover ISBN:  9780821834794 
Product Code:  MMONO/221 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $57.60 
eBook ISBN:  9781470446451 
Product Code:  MMONO/221.E 
List Price:  $67.00 
MAA Member Price:  $60.30 
AMS Member Price:  $53.60 
Softcover ISBN:  9780821834794 
eBookISBN:  9781470446451 
Product Code:  MMONO/221.B 
List Price:  $139.00$105.50 
MAA Member Price:  $125.10$94.95 
AMS Member Price:  $111.20$84.40 

Book DetailsTranslations of Mathematical MonographsVolume: 221; 2003; 142 ppMSC: Primary 53;
The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the threedimensional 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 wellknown 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.ReadershipAdvanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.

Table of Contents

Chapters

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


Additional Material

Reviews

From a review of the Japanese edition: The first thing one notices about this book is that it includes many beautiful pictures of surfaces, which allow the reader to move comfortably through the material. The book takes the reader from historical results through current research … It has distinct charm … the author's research is impressive … has an inviting style that draws the reader to the interesting contents of the book.
translated from Sugaku Expositions


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The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the threedimensional 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 wellknown 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.
Advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.

Chapters

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

From a review of the Japanese edition: The first thing one notices about this book is that it includes many beautiful pictures of surfaces, which allow the reader to move comfortably through the material. The book takes the reader from historical results through current research … It has distinct charm … the author's research is impressive … has an inviting style that draws the reader to the interesting contents of the book.
translated from Sugaku Expositions