Surfaces With Constant Mean Curvature

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Surfaces With Constant Mean Curvature

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Author : Katsuei Kenmotsu
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Surfaces With Constant Mean Curvature written by Katsuei Kenmotsu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

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 objec

Surfaces Of Constant Mean Curvature In Space Forms

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Author : Bennett Palmer
language : en
Publisher:
Release Date : 1986

Surfaces Of Constant Mean Curvature In Space Forms written by Bennett Palmer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

Constant Mean Curvature Surfaces With Boundary

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Author : Rafael López
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-31

Constant Mean Curvature Surfaces With Boundary written by Rafael López and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-31 with Mathematics categories.

The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields. While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs. The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.

Surfaces Of Constant Mean Curvature

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Author : Joseph Albert Wolf
language : en
Publisher:
Release Date : 196?

Surfaces Of Constant Mean Curvature written by Joseph Albert Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 196? with Surfaces of constant curvature categories.

Cyclic Surfaces Of Constant Mean Curvature

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Author : Johannes C. C. Nitsche
language : de
Publisher:
Release Date : 1989

Cyclic Surfaces Of Constant Mean Curvature written by Johannes C. C. Nitsche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Curvature categories.

Contributions To The Theory Of Surfaces Of Constant Mean Curvature

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Author : Eamon Barrett
language : en
Publisher:
Release Date : 1966

Contributions To The Theory Of Surfaces Of Constant Mean Curvature written by Eamon Barrett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Curves on surfaces categories.

Modern Differential Geometry Of Curves And Surfaces With Mathematica

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Author : Elsa Abbena
language : en
Publisher: CRC Press
Release Date : 2017-09-06

Modern Differential Geometry Of Curves And Surfaces With Mathematica written by Elsa Abbena and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-06 with Mathematics categories.

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray’s famous textbook, covers how to define and compute standard geometric functions using Mathematica for constructing new curves and surfaces from existing ones. Since Gray’s death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the Mathematica code and added a Mathematica notebook as an appendix to each chapter. They also address important new topics, such as quaternions. The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi’s formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but Mathematica handles it easily, either through computations or through graphing curvature. Another part of Mathematica that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted. Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use Mathematica to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples. It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.

Differential Geometry Manifolds Curves And Surfaces

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Author : Marcel Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Differential Geometry Manifolds Curves And Surfaces written by Marcel Berger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.

Surfaces Of Constant Mean Curvature In Constant Curvature Manifolds

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Author : D. Hoffmann
language : en
Publisher:
Release Date : 1971

Surfaces Of Constant Mean Curvature In Constant Curvature Manifolds written by D. Hoffmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Surfaces of constant curvature categories.

Infinite Boundary Value Problems For Surfaces Of Constant Mean Curvature

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Author : Joel Spruck
language : en
Publisher:
Release Date : 1971

Infinite Boundary Value Problems For Surfaces Of Constant Mean Curvature written by Joel Spruck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Boundary value problems categories.