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Author : David Williams
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.:/5 (769 download)
Download or read book Construction of Closed Constant Mean Curvature Surfaces written by David Williams and published by . This book was released on 2000 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Lerner
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (753 download)
Download or read book Construction of constant mean curvature surfaces using the DPW representation of harmonic maps written by David Lerner and published by . This book was released on 1993 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : Jesse Ratzkin
Publisher :
ISBN 13 :
Total Pages : 74 pages
Book Rating : 4.:/5 (497 download)
Download or read book An End-to-end Gluing Construction for Surfaces of Constant Mean Curvature written by Jesse Ratzkin and published by . This book was released on 2001 with total page 74 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 : 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 : Zuhal Kucukarslan Yuzbasi
Publisher : Infinite Study
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4./5 ( download)
Download or read book On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group written by Zuhal Kucukarslan Yuzbasi and published by Infinite Study. This book was released on 2022-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Theodora Bourni
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110618362
Total Pages : 149 pages
Book Rating : 4.1/5 (16 download)
Download or read book Mean Curvature Flow written by Theodora Bourni and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-12-07 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by leading experts in geometric analysis, this volume is documenting the material presented in the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, on May 29 - June 1, 2018. The central topic of the 2018 lectures was mean curvature flow, and the material in this volume covers all recent developments in this vibrant area that combines partial differential equations with differential geometry.
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 : Yong He
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (774 download)
Download or read book Constant Mean Curvature Surfaces Bifurcating from Nodoids written by Yong He and published by . This book was released on 2012 with total page 0 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 : Karsten Grosse-Brauckmann
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (756 download)
Download or read book Stable constant mean curvature surfaces minimize area written by Karsten Grosse-Brauckmann and published by . This book was released on 1995 with total page 8 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:
Download or read book Properness Results for Constant Mean Curvature Surfaces written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Karsten Grosse-Brauckmann
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.:/5 (17 download)
Download or read book Complete embedded constant mean curvature surfaces written by Karsten Grosse-Brauckmann and published by . This book was released on 1998 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frederic Hélein
Publisher : Birkhäuser
ISBN 13 : 3034883307
Total Pages : 123 pages
Book Rating : 4.0/5 (348 download)
Download or read book Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems written by Frederic Hélein and published by Birkhäuser. This book was released on 2012-12-06 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
