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Author : Marcos Dajczer
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (254 download)
Download or read book Constant Mean Curvature Hypersurfaces in Warped Product Spaces written by Marcos Dajczer and published by . This book was released on 2005 with total page 17 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 : 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 : Jesus A Alvarez Lopez
Publisher : World Scientific
ISBN 13 : 9814468460
Total Pages : 343 pages
Book Rating : 4.8/5 (144 download)
Download or read book Differential Geometry - Proceedings Of The Viii International Colloquium written by Jesus A Alvarez Lopez and published by World Scientific. This book was released on 2009-04-27 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository papers on recent advances in foliations and Riemannian geometry. Some of the topics covered in this volume include: topology, geometry, dynamics and analysis of foliations, curvature, submanifold theory, Lie groups and harmonic maps.Among the contributions, readers may find an extensive survey on characteristic classes of Riemannian foliations offering also new results, an article showing the uniform simplicity of certain diffeomorphism groups, an exposition of convergences of contact structures to foliations from the point of view of Thurston's and Thurston-Bennequin's inequalities, a discussion about Fatou-Julia decompositions for foliations and a description of singular Riemannian foliations on spaces without conjugate points.Papers on submanifold theory focus on the existence of graphs with prescribed mean curvature and mean curvature flow for spacelike graphs, isometric and conformal deformations and detailed surveys on totally geodesic submanifolds in symmetric spaces, cohomogeneity one actions on hyperbolic spaces and rigidity of geodesic spheres in space forms. Geometric realizability of curvature tensors and curvature operators are also treated in this volume with special attention to the affine and the pseudo-Riemannian settings. Also, some contributions on biharmonic maps and submanifolds enrich the scope of this volume in providing an overview of different topics of current interest in differential geometry.
Author : Thomas Hasanis
Publisher :
ISBN 13 :
Total Pages : 80 pages
Book Rating : 4.:/5 (989 download)
Download or read book Hypersurfaces with Constant Scalar Curvature and Constant Mean Curvature written by Thomas Hasanis and published by . This book was released on 1991 with total page 80 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 : Bang-yen Chen
Publisher : World Scientific
ISBN 13 : 9813208945
Total Pages : 517 pages
Book Rating : 4.8/5 (132 download)
Download or read book Differential Geometry Of Warped Product Manifolds And Submanifolds written by Bang-yen Chen and published by World Scientific. This book was released on 2017-05-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Author : Walter Iaan Seaman
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.:/5 (266 download)
Download or read book Hypersurfaces of Constant Mean Curvature in Euclidean Space and Groups of Heisenberg Type written by Walter Iaan Seaman and published by . This book was released on 1982 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jie Wu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (931 download)
Download or read book On Rigidity of Hypersurfaces with Constant Curvature Functions in Warped Product Manifolds written by Jie Wu and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ronaldo Freire
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (467 download)
Download or read book Hypersurfaces with Constant Mean Curvature and Bounded Scalar Curvature in Euclidean and Hyperbolic Space written by Ronaldo Freire and published by . This book was released on 2000 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank Duzaar
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (221 download)
Download or read book Hypersurfaces with Constant Mean Curvature and Prescribed Area written by Frank Duzaar and published by . This book was released on 1995 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Manuel Ritoré
Publisher : Springer Nature
ISBN 13 : 3031379012
Total Pages : 470 pages
Book Rating : 4.0/5 (313 download)
Download or read book Isoperimetric Inequalities in Riemannian Manifolds written by Manuel Ritoré and published by Springer Nature. This book was released on 2023-10-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.
Author : Jorge Herbert Soares De Lira
Publisher : de Gruyter
ISBN 13 : 9783110359862
Total Pages : 300 pages
Book Rating : 4.3/5 (598 download)
Download or read book Variational Problems for Hypersurfaces in Riemannian Manifolds written by Jorge Herbert Soares De Lira and published by de Gruyter. This book was released on 2017-07-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric analysis is one of the most active research fields nowadays. The interplay between geometric and analytic techniques is at the core of recent remarkable advances in differential geometry and topology. This book is aimed to be a comprehensive introduction to the basic geometric facts and PDE tools as well as to some current research topics on hypersurfaces with prescribed mean curvature in Riemannian manifolds.
Author : Carlos Edgard Harle
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (34 download)
Download or read book Rigidity of Hypersurfaces of Constant Scalar Curvature written by Carlos Edgard Harle and published by . This book was released on 1969 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marcos Petrucio de A. Cavalcante
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (687 download)
Download or read book Conformally Flat Metrics, Constant Mean Curvature Surfaces in Product Spaces and R-stability of Hypersurfaces written by Marcos Petrucio de A. Cavalcante and published by . This book was released on 2006 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul Baird
Publisher : Oxford University Press
ISBN 13 : 9780198503620
Total Pages : 540 pages
Book Rating : 4.5/5 (36 download)
Download or read book Harmonic Morphisms Between Riemannian Manifolds written by Paul Baird and published by Oxford University Press. This book was released on 2003 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Author : Manuel Ritoré
Publisher : Springer Science & Business Media
ISBN 13 : 3034602138
Total Pages : 113 pages
Book Rating : 4.0/5 (346 download)
Download or read book Mean Curvature Flow and Isoperimetric Inequalities written by Manuel Ritoré and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
