Surfaces with Constant Mean Curvature

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.

ISBN 0821834797   Pages 142 ISBN13 9780821834794 (What's this?)   Volumes 001 Publisher American Mathematical Society   Weight (grammes) 186 Imprint American Mathematical Society   Published in Providence Format Paperback   Series ISSN 0065-928 Publication date 15 Oct 2003   Series title Translations of Mathematical Monographs Library of Congress QA644.K461   Height (mm) 230 DEWEY 516.362   Academic level Professional / Scholarly DEWEY edition DC22

		Foreword
Ch. 1		Preliminaries from the Theory of Surfaces		1
Ch. 2		Mean Curvature		25
Ch. 3		Rotational Surfaces		39
Ch. 4		Helicoidal Surfaces		53
Ch. 5		Stability		63
Ch. 6		Tori		75
Ch. 7		The Balancing Formula		83
Ch. 8		The Gauss Map		97
Ch. 9		Intricate Constant Mean Curvature Surfaces		109
		App. A: Supplement		121
		App. B: Programs for the Figures		127
		Postscript		133
		Bibliography		137
		List of Sources for the Figures		139
		Index		141

 Be the first to write a customer review