Constant Mean Curvature Surfaces Of Revolution And Their Stability
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Author | : Nahid Sultana |
Publisher | : LAP Lambert Academic Publishing |
Total Pages | : 112 |
Release | : 2014-02 |
Genre | : |
ISBN | : 9783848481538 |
Download Constant Mean Curvature Surfaces of Revolution and Their Stability Book in PDF, Epub and Kindle
The field of Constant Mean Curvature (CMC) surfaces had its beginning in the nineteenth century with the works of Riemann, Weierstrass and Enneper. Recently it has enjoyed a surge of growth due to the advent of computer graphics. This field has applications in many applied fields such as applied physics, polymer science, architecture, and computer graphics. The method for the construction of CMC surfaces was developed by J. Dorfmeister, F. Pedit, and H. Wu; it is commonly called the DPW method. The DPW method is a Weierstrass type representation for CMC surfaces, using techniques of integrable systems. It gives an algorithm to compute all CMC surfaces. This book includes: explicit conformal parametrizations of CMC surfaces of revolution, in each of the three space forms Euclidean 3-space, spherical 3-space and hyperbolic 3-space by using the DPW method; the lower bounds for the Morse index and nullity of CMC tori of revolution in the 3-sphere; the spectra of Jacobi operators for CMC tori of revolution in the 3-sphere; stability properties of CMC surfaces of revolution in general simply-connected spherically symmetric 3-spaces, and in the particular case of Schwarzschild space.
Author | : Katsuei Kenmotsu |
Publisher | : American Mathematical Soc. |
Total Pages | : 156 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9780821834794 |
Download Surfaces with Constant Mean Curvature Book in PDF, Epub and Kindle
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.
Author | : N. Koiso |
Publisher | : |
Total Pages | : 29 |
Release | : 1987 |
Genre | : |
ISBN | : |
Download Stability of Surfaces with Constant Mean Curvature in $R 3$ Book in PDF, Epub and Kindle
Author | : Miyuki Koiso |
Publisher | : |
Total Pages | : 29 |
Release | : 1987 |
Genre | : |
ISBN | : |
Download Stability of surfaces with constant mean curvature in IR3 Book in PDF, Epub and Kindle
Author | : Steffen Fröhlich |
Publisher | : |
Total Pages | : 7 |
Release | : 2002 |
Genre | : |
ISBN | : |
Download A Note on My-stable Surfaces with Prescribed Constant Mean Curvature Book in PDF, Epub and Kindle
Author | : Société mathématique de France. Journées |
Publisher | : |
Total Pages | : 94 |
Release | : 1993 |
Genre | : Calculus of variations |
ISBN | : |
Download Soap Bubble Clusters and Constant Mean Curvature Surfaces Book in PDF, Epub and Kindle
Author | : Leung-Fu Cheung |
Publisher | : |
Total Pages | : 88 |
Release | : 1991 |
Genre | : Geometry, Differential |
ISBN | : |
Download Geometric Properties of Stable Noncompact Constant Mean Curvature Surfaces Book in PDF, Epub and Kindle
Author | : João Lucas Marques Barbosa |
Publisher | : |
Total Pages | : 26 |
Release | : 1983 |
Genre | : |
ISBN | : |
Download Stability of Hypersurfaces with Constant Mean Curvature Book in PDF, Epub and Kindle
Author | : A. T. Fomenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 364 |
Release | : 1993 |
Genre | : Minimal surfaces |
ISBN | : 9780821841167 |
Download Minimal Surfaces Book in PDF, Epub and Kindle
This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.
Author | : Steffen Fröhlich |
Publisher | : |
Total Pages | : |
Release | : 2002 |
Genre | : |
ISBN | : |
Download A Note on [mu]-stable Surfaces with Prescribed Constant Mean Curvature Book in PDF, Epub and Kindle