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 objects. The book is suitable for advanced undergraduates, graduate students and research mathematicians interested in analysis and differential geometry.

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.

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.

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.

On Parametric Surfaces With Constant Mean Curvature Along Given Smarandache Curves In Lie Group

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Author : Zuhal Kucukarslan Yuzbasi
language : en
Publisher: Infinite Study
Release Date : 2022-01-01

On Parametric Surfaces With Constant Mean Curvature Along Given Smarandache Curves In Lie Group written by Zuhal Kucukarslan Yuzbasi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.

This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.

Surfaces With Constant Mean Curvature

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Author : Lawrence E. Schmidt
language : en
Publisher:
Release Date : 19??

Surfaces With Constant Mean Curvature written by Lawrence E. Schmidt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 19?? with Surfaces categories.

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.

Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems

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Author : Frederic Hélein
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems written by Frederic Hélein and has been published by Birkhäuser 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 intends to give an introduction to harmonic maps between a surface and a symmetric manifold and constant mean curvature surfaces as completely integrable systems. The presentation is accessible to undergraduate and graduate students in mathematics but will also be useful to researchers. It is among the first textbooks about integrable systems, their interplay with harmonic maps and the use of loop groups, and it presents the theory, for the first time, from the point of view of a differential geometer. The most important results are exposed with complete proofs (except for the last two chapters, which require a minimal knowledge from the reader). Some proofs have been completely rewritten with the objective, in particular, to clarify the relation between finite mean curvature tori, Wente tori and the loop group approach - an aspect largely neglected in the literature. The book helps the reader to access the ideas of the theory and to acquire a unified perspective of the subject.

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.

On Nonparametric Surfaces Of Constant Mean Curvature

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Author : Fei-tsen Liang
language : en
Publisher:
Release Date : 1986

On Nonparametric Surfaces Of Constant Mean Curvature written by Fei-tsen Liang 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.