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Author : Bennett Palmer
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.F/5 ( download)
Download or read book Surfaces of Constant Mean Curvature in Space Forms written by Bennett Palmer and published by . This book was released on 1986 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Julia Plehnert
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832532064
Total Pages : 94 pages
Book Rating : 4.8/5 (325 download)
Download or read book Constant Mean Curvature Surfaces in Homogeneous Manifolds written by Julia Plehnert and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC H surfaces in ∑(k) x R with H ∈ [0,1/2] and k + 4H2 ≤ 0, has genus 0,2 k ends and k-fold dihedral symmetry, k ≥ 2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1/2 surface in H2 ∈ R with k ends, genus 1 and k-fold dihedral symmetry, k ≥ 3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1/2 all surfaces are Alexandrov-embedded.
Author : Sungwook Lee
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (521 download)
Download or read book Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31 written by Sungwook Lee and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Eamon Barrett
Publisher :
ISBN 13 :
Total Pages : 230 pages
Book Rating : 4.F/5 ( download)
Download or read book Contributions to the Theory of Surfaces of Constant Mean Curvature written by Eamon Barrett and published by . This book was released on 1966 with total page 230 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 : 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 : 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 : Ioannis Markos Roussos
Publisher :
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.:/5 (319 download)
Download or read book Mean-curvature-preserving Isometries of Surfaces in Ordinary Space written by Ioannis Markos Roussos and published by . This book was released on 1986 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lawrence E. Schmidt
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (214 download)
Download or read book Surfaces with Constant Mean Curvature written by Lawrence E. Schmidt and published by . This book was released on 19?? with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bennett Palmer
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (461 download)
Download or read book Spacelike constant mean curvature surfaces in pseudo-Riemannian space forms written by Bennett Palmer and published by . This book was released on 1987 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Áurea Casinhas Quintino
Publisher : Cambridge University Press
ISBN 13 : 1108794424
Total Pages : 261 pages
Book Rating : 4.1/5 (87 download)
Download or read book Constrained Willmore Surfaces written by Áurea Casinhas Quintino and published by Cambridge University Press. This book was released on 2021-06-10 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.
Author : Sungwook Lee
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (521 download)
Download or read book Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31 written by Sungwook Lee and published by . This book was released on 2002 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Joseph Albert Wolf
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (279 download)
Download or read book Surfaces of Constant Mean Curvature written by Joseph Albert Wolf and published by . This book was released on 196? with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Elsa Abbena
Publisher : CRC Press
ISBN 13 : 142001031X
Total Pages : 1016 pages
Book Rating : 4.4/5 (2 download)
Download or read book Modern Differential Geometry of Curves and Surfaces with Mathematica written by Elsa Abbena and published by CRC Press. This book was released on 2017-09-06 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
