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Author : Michael Struwe
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (46 download)
Download or read book The existence of surfaces of constant mean curvature with free boundaries written by Michael Struwe and published by . This book was released on 1986 with total page 49 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 : 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 : 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 : Frank Duzaar
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (11 download)
Download or read book On the Existence of Surfaces with Prescribed Mean Curvature and Boundary in Higher Dimensions written by Frank Duzaar and published by . This book was released on 1994 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Struwe
Publisher : Springer Science & Business Media
ISBN 13 : 3662041944
Total Pages : 292 pages
Book Rating : 4.6/5 (62 download)
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3642117007
Total Pages : 634 pages
Book Rating : 4.6/5 (421 download)
Download or read book Regularity of Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau ́s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau ́s problem have no interior branch points.
Author : Paul Concus
Publisher : Springer Science & Business Media
ISBN 13 : 1461246563
Total Pages : 201 pages
Book Rating : 4.4/5 (612 download)
Download or read book Variational Methods for Free Surface Interfaces written by Paul Concus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vallombrosa Center was host during the week September 7-12, 1985 to about 40 mathematicians, physical scientists, and engineers, who share a common interest in free surface phenomena. This volume includes a selection of contributions by participants and also a few papers by interested scientists who were unable to attend in person. Although a proceedings volume cannot recapture entirely the stimulus of personal interaction that ultimately is the best justification for such a gathering, we do offer what we hope is a representative sampling of the contributions, indicating something of the varied and interrelated ways with which these classical but largely unsettled questions are currently being attacked. For the participants, and also for other specialists, the 23 papers that follow should help to establish and to maintain the new ideas and insights that were presented, as active working tools. Much of the material will certainly be of interest also for a broader audience, as it impinges and overlaps with varying directions of scientific development. On behalf of the organizing committee, we thank the speakers for excellent, well-prepared lectures. Additionally, the many lively informal discussions did much to contribute to the success of the conference.
Author : Maria Athanassenas
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (46 download)
Download or read book A variational problem for constant mean curvature surfaces with free boundary written by Maria Athanassenas and published by . This book was released on 1986 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3642117066
Total Pages : 547 pages
Book Rating : 4.6/5 (421 download)
Download or read book Global Analysis of Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of "edge-crawling" along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a "global theory of minimal surfaces" as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmüller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau ́s problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented.
Author : Paul H. Rabinowitz
Publisher : Academic Press
ISBN 13 : 1483268861
Total Pages : 707 pages
Book Rating : 4.4/5 (832 download)
Download or read book Analysis, et Cetera written by Paul H. Rabinowitz and published by Academic Press. This book was released on 2014-05-10 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, et cetera: Research Papers Published in Honor of Jürgen Moser's 60th Birthday provides a collection of papers dedicated to Jürgen Moser on the occasion of his 60th birthday. This book covers a variety of topics, including Helmholtz equation, algebraic complex integrability, theory of Lie groups, and trigonometric polynomials. Organized into 31 chapters, this book begins with an overview of some basic consequences of the definition of algebraic complete integrability. This text then derives a representation theorem for solutions of the Helmholtz equation. Other chapters consider the integrable generalizations of the Volterra system and explain the dynamical system in the finite-dimensional case. This book discusses as well the global periodic solutions for the planar triple pendulum. The final chapter deals with the problem of deriving the macroscopic conservation laws, or the Euler equations, in accurate fashion from the microscopic equations of classical mechanics. This book is a valuable resource for mathematicians.
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 : Stefan Hildebrandt
Publisher : Springer
ISBN 13 : 3540460241
Total Pages : 433 pages
Book Rating : 4.5/5 (44 download)
Download or read book Partial Differential Equations and Calculus of Variations written by Stefan Hildebrandt and published by Springer. This book was released on 2006-11-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Author : James Eells
Publisher : World Scientific
ISBN 13 : 9814502928
Total Pages : 229 pages
Book Rating : 4.8/5 (145 download)
Download or read book Two Reports On Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1995-03-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.
Author : Michael Grüter
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (459 download)
Download or read book Regularity for stationary surfaces of constant mean curvature with free boundaries written by Michael Grüter and published by . This book was released on 1984 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3642116981
Total Pages : 699 pages
Book Rating : 4.6/5 (421 download)
Download or read book Minimal Surfaces written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2010-08-16 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Björling ́s initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau ́s problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche ́s uniqueness theorem and Tomi ́s finiteness result. In addition, a theory of unstable solutions of Plateau ́s problems is developed which is based on Courant ́s mountain pass lemma. Furthermore, Dirichlet ́s problem for nonparametric H-surfaces is solved, using the solution of Plateau ́s problem for H-surfaces and the pertinent estimates.
Author : Jin-Tzu Chen
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.F/5 ( download)
Download or read book On the Existence of Capillary Free Surfaces in the Absence of Gravity written by Jin-Tzu Chen and published by . This book was released on 1979 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
