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Author : Wayne Rossman
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (272 download)
Download or read book Constant Mean Curvature Surfaces in Euclidean and Hyperbolic 3-space written by Wayne Rossman and published by . This book was released on 1992 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yoshihiro Tonegawa
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.:/5 (822 download)
Download or read book Complete Constant Mean Curvature Surfaces in Hyperbolic Space written by Yoshihiro Tonegawa and published by . This book was released on 1993 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierre H. Bérard
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (258 download)
Download or read book The Index of Constant Mean Curvature Surfaces in Hyperbolic 3-spaces written by Pierre H. Bérard and published by . This book was released on 1994 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nahid Sultana
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783848481538
Total Pages : 112 pages
Book Rating : 4.4/5 (815 download)
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.
Author : Katsuei Kenmotsu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821834794
Total Pages : 156 pages
Book Rating : 4.8/5 (347 download)
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.
Author : S.N. Krivoshapko
Publisher : Springer
ISBN 13 : 3319117734
Total Pages : 761 pages
Book Rating : 4.3/5 (191 download)
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.
Author : Rafael López
Publisher : Springer Science & Business Media
ISBN 13 : 3642396267
Total Pages : 296 pages
Book Rating : 4.6/5 (423 download)
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.
Author : Ronaldo Freire
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (467 download)
Download or read book Hypersurfaces with Constant Mean Curvature and Bounded Scalar Curvature in Euclidean and Hyperbolic Space written by Ronaldo Freire and published by . This book was released on 2000 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gary Lynn Kerbaugh
Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (849 download)
Download or read book Surfaces of Constant Mean Curvature One in Hyperbolic Space written by Gary Lynn Kerbaugh and published by . This book was released on 1985 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (916 download)
Download or read book Constant mean curvature H 1 surfaces in hyperbolic space written by and published by . This book was released on 1992 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Catherine MacCune
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (54 download)
Download or read book An Analogue of the UP-iteration for Constant Mean Curvature One Surfaces in Hyperbolic 3-space written by Catherine MacCune and published by . This book was released on 2000 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henry C. Wente
Publisher : American Mathematical Soc.
ISBN 13 : 0821825364
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)
Download or read book Constant Mean Curvature Immersions of Enneper Type written by Henry C. Wente and published by American Mathematical Soc.. This book was released on 1992 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is devoted to the case of constant mean curvature surfaces immersed in [bold]R3. We reduce this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in [bold]R3 with embedded Delaunay ends and [italic]n-lobes in the middle, and one-parameter families of immersed constant mean curvature tori in [bold]R3. We examine minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.
Author : Jonas de M. Gomes
Publisher :
ISBN 13 :
Total Pages : 51 pages
Book Rating : 4.:/5 (636 download)
Download or read book On Surfaces of Constant Mean Curvature in Hyperbolic Space written by Jonas de M. Gomes and published by . This book was released on 1985 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W.H. III Meeks
Publisher : Springer
ISBN 13 : 3540456090
Total Pages : 126 pages
Book Rating : 4.5/5 (44 download)
Download or read book The Global Theory of Minimal Surfaces in Flat Spaces written by W.H. III Meeks and published by Springer. This book was released on 2004-10-11 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
Author : Ahmat T. Ali
Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)
Download or read book Ruled Surfaces generated by special curves in Eucleadean 3-Space written by Ahmat T. Ali and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of Eucleadean 3-Spase is investigated.
Author : Manuel Ritoré
Publisher : Springer Science & Business Media
ISBN 13 : 3034602138
Total Pages : 113 pages
Book Rating : 4.0/5 (346 download)
Download or read book Mean Curvature Flow and Isoperimetric Inequalities written by Manuel Ritoré and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Author : Saeid Nazari
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.:/5 (33 download)
Download or read book Rotational Surfaces in Euclidean and Hyperbolic Spaces, Mean Curvature Motion, and the Moving Finite Element Method written by Saeid Nazari and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
