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Author : K. Yamada
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (897 download)
Download or read book Complete Space-like Surfaces in the Minkowski 3-space with Constant Mean Curvature written by K. Yamada and published by . This book was released on 1987 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kotaro Yamada
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (461 download)
Download or read book Complete space-like surfaces in the Minkowski 3-space with constant mean curvature written by Kotaro Yamada and published by . This book was released on 1987 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shane B. Dowdall
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (87 download)
Download or read book Spacelike Surfaces of Constant Mean Curvature Having Continuous Internal Symmetry in Minkowski Three Space written by Shane B. Dowdall and published by . This book was released on 1996 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Andrejs Treibergs
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.F/5 ( download)
Download or read book Entire Spacelike Hypersurfaces of Constant Mean Curvature in Minkowski Space written by Andrejs Treibergs and published by . This book was released on 1980 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Jamie Patrick Lambert
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (941 download)
Download or read book Lorentz Invariant Spacelike Surfaces with Constant Mean Curvature in Anti-de Sitter 3-space written by Jamie Patrick Lambert and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space [mathematical formula] of constant curvature [mathematical element]. In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in [mathematical formula]. I also studied the limit behavior of those constant mean curvature c surfaces in [mathematical formula]. It turns out that they approach a maximal catenoid in Minkowski 3-space [mathematical element]. The limit maximal catenoid is Lorentz invariant in [mathematical element]. --Page ii.
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 : Olga Gil-medrano
Publisher : World Scientific
ISBN 13 : 9814488917
Total Pages : 324 pages
Book Rating : 4.8/5 (144 download)
Download or read book Differential Geometry, Valencia 2001 - Procs Of The Intl Conf Held To Honour The 60th Birthday Of A M Naveira written by Olga Gil-medrano and published by World Scientific. This book was released on 2002-07-18 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as Willmore-Chen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with finite total curvature.
Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
ISBN 13 : 0821839888
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)
Download or read book Differential Geometry written by Wolfgang Kühnel and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
Author : Tom Yau-Heng Wan
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.F/5 ( download)
Download or read book Constant Mean Curvature Surface, Harmonic Map and Universal Teichmüller Space written by Tom Yau-Heng Wan and published by . This book was released on 1991 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Olga Gil-Medrano
Publisher : World Scientific
ISBN 13 : 9810249063
Total Pages : 324 pages
Book Rating : 4.8/5 (12 download)
Download or read book Differential Geometry, Valencia 2001 written by Olga Gil-Medrano and published by World Scientific. This book was released on 2002 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a conference on differential geometry held in honour of the 60th birthday of A M Naveira. The meeting brought together distinguished researchers from a variety of areas in Riemannian geometry. The topics include: geometry of the curvature tensor, variational problems for geometric functionals such as Willmore-Chen tension, volume and energy of foliations and vector fields, and energy of maps. Many papers concern special submanifolds in Riemannian and Lorentzian manifolds, such as those with constant mean (scalar, Gauss, etc.) curvature and those with finite total curvature.
Author : Luis J. Alías
Publisher : Springer
ISBN 13 : 3319243373
Total Pages : 594 pages
Book Rating : 4.3/5 (192 download)
Download or read book Maximum Principles and Geometric Applications written by Luis J. Alías and published by Springer. This book was released on 2016-02-13 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on. Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.
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 : Shing-tung Yau
Publisher : Princeton University Press
ISBN 13 : 1400881919
Total Pages : 720 pages
Book Rating : 4.4/5 (8 download)
Download or read book Seminar on Differential Geometry. (AM-102), Volume 102 written by Shing-tung Yau and published by Princeton University Press. This book was released on 2016-03-02 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.
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 : Christopher Kum Anand
Publisher : CRC Press
ISBN 13 : 9781584880325
Total Pages : 332 pages
Book Rating : 4.8/5 (83 download)
Download or read book Harmonic Morphisms, Harmonic Maps and Related Topics written by Christopher Kum Anand and published by CRC Press. This book was released on 1999-10-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.
