Constant Mean Curvature Surfaces With Boundary

Author : Rafael López
Publisher : Springer Science & Business Media
ISBN 13 : 3642396267
Total Pages : 296 pages
Book Rating : 4.67/5 ( download)

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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 : Katsuei Kenmotsu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821834794
Total Pages : 156 pages
Book Rating : 4.97/5 ( download)

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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 : Joel Spruck
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.08/5 ( download)

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Download or read book Infinite Boundary Value Problems for Surfaces of Constant Mean Curvature written by Joel Spruck and published by . This book was released on 1971 with total page 152 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 : 4.62/5 ( download)

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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 : Kenneth A. Brakke
Publisher : Princeton University Press
ISBN 13 : 1400867436
Total Pages : 258 pages
Book Rating : 4.31/5 ( download)

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Download or read book The Motion of a Surface by Its Mean Curvature. (MN-20) written by Kenneth A. Brakke and published by Princeton University Press. This book was released on 2015-03-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of a surface by its mean curvature. This mathematical description encompasses, among other subtleties, those of changing geometries and instantaneous mass losses. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Robert Osserman
Publisher : Courier Corporation
ISBN 13 : 0486167690
Total Pages : 224 pages
Book Rating : 4.95/5 ( download)

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Download or read book A Survey of Minimal Surfaces written by Robert Osserman and published by Courier Corporation. This book was released on 2013-12-10 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.

Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3662027917
Total Pages : 528 pages
Book Rating : 4.12/5 ( download)

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Download or read book Minimal Surfaces I written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.

Author : Frederic Helein
Publisher :
ISBN 13 : 9783034883313
Total Pages : 124 pages
Book Rating : 4.15/5 ( download)

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Download or read book Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems written by Frederic Helein and published by . This book was released on 2001-06-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bennett Palmer
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.03/5 ( download)

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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 : Fei-tsen Liang
Publisher :
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.44/5 ( download)

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Download or read book On Nonparametric Surfaces of Constant Mean Curvature written by Fei-tsen Liang and published by . This book was released on 1986 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: