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Constant Mean Curvature Surfaces Of Revolution And Their Stability
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Book Synopsis Constant Mean Curvature Surfaces of Revolution and Their Stability by : Nahid Sultana
Download or read book Constant Mean Curvature Surfaces of Revolution and Their Stability written by Nahid Sultana and published by LAP Lambert Academic Publishing. This book was released on 2014-02 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surfaces with Constant Mean Curvature by : Katsuei Kenmotsu
Download or read book Surfaces with Constant Mean Curvature written by Katsuei Kenmotsu and published by American Mathematical Soc.. This book was released on 2003 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability of Surfaces with Constant Mean Curvature in $R 3$ by : N. Koiso
Download or read book Stability of Surfaces with Constant Mean Curvature in $R 3$ written by N. Koiso and published by . This book was released on 1987 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of surfaces with constant mean curvature in IR3 by : Miyuki Koiso
Download or read book Stability of surfaces with constant mean curvature in IR3 written by Miyuki Koiso and published by . This book was released on 1987 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Note on My-stable Surfaces with Prescribed Constant Mean Curvature by : Steffen Fröhlich
Download or read book A Note on My-stable Surfaces with Prescribed Constant Mean Curvature written by Steffen Fröhlich and published by . This book was released on 2002 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Soap Bubble Clusters and Constant Mean Curvature Surfaces by : Société mathématique de France. Journées
Download or read book Soap Bubble Clusters and Constant Mean Curvature Surfaces written by Société mathématique de France. Journées and published by . This book was released on 1993 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Properties of Stable Noncompact Constant Mean Curvature Surfaces by : Leung-Fu Cheung
Download or read book Geometric Properties of Stable Noncompact Constant Mean Curvature Surfaces written by Leung-Fu Cheung and published by . This book was released on 1991 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Hypersurfaces with Constant Mean Curvature by : João Lucas Marques Barbosa
Download or read book Stability of Hypersurfaces with Constant Mean Curvature written by João Lucas Marques Barbosa and published by . This book was released on 1983 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Minimal Surfaces written by A. T. Fomenko and published by American Mathematical Soc.. This book was released on 1993 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Note on [mu]-stable Surfaces with Prescribed Constant Mean Curvature by : Steffen Fröhlich
Download or read book A Note on [mu]-stable Surfaces with Prescribed Constant Mean Curvature written by Steffen Fröhlich and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Constant Mean Curvature Surfaces with Boundary by : Rafael López
Download or read book Constant Mean Curvature Surfaces with Boundary written by Rafael López and published by Springer Science & Business Media. This book was released on 2013-08-31 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Manfredo P. do Carmo – Selected Papers by : Manfredo P. do Carmo
Download or read book Manfredo P. do Carmo – Selected Papers written by Manfredo P. do Carmo and published by Springer Science & Business Media. This book was released on 2012-04-02 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.
Book Synopsis A Survey of Minimal Surfaces by : Robert Osserman
Download or read book A Survey of Minimal Surfaces written by Robert Osserman and published by Courier Corporation. This book was released on 1986-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This clear and comprehensive study features 12 sections that discuss parametric and non-parametric surfaces, surfaces that minimize area, isothermal parameters, Bernstein's theorem, minimal surfaces with boundary, and many other topics. This revised edition includes material on minimal surfaces in relativity and topology and updated work on Plateau's problem and isoperimetric inequalities. 1969 edition.
Book Synopsis Symposium on the Differential Geometry of Submanifolds by : Luc Vrancken
Download or read book Symposium on the Differential Geometry of Submanifolds written by Luc Vrancken and published by Lulu.com. This book was released on 2008-06-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).
Book Synopsis Encyclopedia of Analytical Surfaces by : S.N. Krivoshapko
Download or read book Encyclopedia of Analytical Surfaces written by S.N. Krivoshapko and published by Springer. This book was released on 2015-02-25 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.
Book Synopsis Discrete Constant Mean Curvature Surfaces and Their Index by : Konrad Polthier
Download or read book Discrete Constant Mean Curvature Surfaces and Their Index written by Konrad Polthier and published by . This book was released on 2000 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Geometry of Submanifolds by : K. Kenmotsu
Download or read book Differential Geometry of Submanifolds written by K. Kenmotsu and published by Springer. This book was released on 2007-01-05 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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