Surfaces with Constant Mean CurvatureShare this page
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.
Table of Contents
Table of Contents
Surfaces with Constant Mean Curvature
Advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.
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