Surfaces with constant mean curvature
By: Katsuei Kenmotsu ; translated by Katsuhiro Moriya.
Series: Translations of mathematical monographs -- v. 221.
Publisher: American Mathematical Society
Published: 2003
Place of publication: Providence, R.I
Language: eng
Number of pages: 142
Subjects: Minimal surfaces.; Curvature.; Geometry, Differential.
Work titles: Kyokumenron kōgi.
Description: "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. 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. A trivial 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." "In this book, the author presents the numerous examples of constant mean curvature surfaces and the techniques for studying them. Many figures illustrate the presented results and allow the reader to visualize and better understand these beautiful objects."--BOOK JACKET.
Notes: Includes bibliographical references (p. 137-138) and index.