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Author : Leon Simon
Publisher :
ISBN 13 :
Total Pages : 210 pages
Book Rating : 4.3/5 (91 download)
Download or read book Miniconference on Geometry and Partial Differential Equations, 2 written by Leon Simon and published by . This book was released on 1987 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leon Simon
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.:/5 (41 download)
Download or read book Miniconference on Geometry and Partial Differential Equations written by Leon Simon and published by . This book was released on 1986 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : World Scientific
ISBN 13 :
Total Pages : 1191 pages
Book Rating : 4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1191 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bennett Chow
Publisher : American Mathematical Society
ISBN 13 : 1470478048
Total Pages : 753 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lectures on Differential Geometry written by Bennett Chow and published by American Mathematical Society. This book was released on 2024-10-07 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern?Gauss?Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincar‚ and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds. The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.
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.
Author : Benson Farb
Publisher : American Mathematical Society
ISBN 13 : 1470474735
Total Pages : 652 pages
Book Rating : 4.4/5 (74 download)
Download or read book Collected Works of William P. Thurston with Commentary written by Benson Farb and published by American Mathematical Society. This book was released on 2023-06-02 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume II contains William Thurston's papers on the geometry and topology of 3-manifolds, on complexity, constructions and computers, and on geometric group theory.
Author : Rajendra Bhatia
Publisher : World Scientific
ISBN 13 : 9814462934
Total Pages : 4137 pages
Book Rating : 4.8/5 (144 download)
Download or read book Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Author : William Fitzgibbon
Publisher : Springer
ISBN 13 : 940179054X
Total Pages : 252 pages
Book Rating : 4.4/5 (17 download)
Download or read book Modeling, Simulation and Optimization for Science and Technology written by William Fitzgibbon and published by Springer. This book was released on 2014-06-18 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains thirteen articles on advances in applied mathematics and computing methods for engineering problems. Six papers are on optimization methods and algorithms with emphasis on problems with multiple criteria; four articles are on numerical methods for applied problems modeled with nonlinear PDEs; two contributions are on abstract estimates for error analysis; finally one paper deals with rare events in the context of uncertainty quantification. Applications include aerospace, glaciology and nonlinear elasticity. Herein is a selection of contributions from speakers at two conferences on applied mathematics held in June 2012 at the University of Jyväskylä, Finland. The first conference, “Optimization and PDEs with Industrial Applications” celebrated the seventieth birthday of Professor Jacques Périaux of the University of Jyväskylä and Polytechnic University of Catalonia (Barcelona Tech) and the second conference, “Optimization and PDEs with Applications” celebrated the seventy-fifth birthday of Professor Roland Glowinski of the University of Houston. This work should be of interest to researchers and practitioners as well as advanced students or engineers in computational and applied mathematics or mechanics.
Author : Peter B. Gilkey
Publisher : CRC Press
ISBN 13 : 9780849382772
Total Pages : 294 pages
Book Rating : 4.3/5 (827 download)
Download or read book Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture written by Peter B. Gilkey and published by CRC Press. This book was released on 1999-07-27 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and pi: Z ® Y is a Riemannian submersion. After providing the necessary background, including basic differential geometry and a discussion of Laplace type operators, the authors address rigidity theorems. They establish conditions that ensure that the pull back of every eigenform on Y is an eigenform on Z so the eigenvalues do not change, then show that if a single eigensection is preserved, the eigenvalues do not change for the scalar or Bochner Laplacians. For the form valued Laplacian, they show that if an eigenform is preserved, then the corresponding eigenvalue can only increase. They generalize these results to the complex setting as well. However, the spinor setting is quite different. For a manifold with non-trivial boundary and imposed Neumann boundary conditions, the result is surprising-the eigenvalues can change. Although this is a relatively rare phenomenon, the authors give examples-a circle bundle or, more generally, a principal bundle with structure group G where the first cohomology group H1(G;R) is non trivial. They show similar results in the complex setting, show that eigenvalues can decrease in the spinor setting, and offer a list of unsolved problems in this area. Moving to some related topics involving questions of positive curvature, for the first time in mathematical literature the authors establish a link between the spectral geometry of Riemannian submersions and the Gromov-Lawson conjecture. Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture addresses a hot research area and promises to set a standard for the field. Researchers and applied mathematicians interested in mathematical physics and relativity will find this work both fascinating and important.
Author : Yasunori Maekawa
Publisher : Springer
ISBN 13 : 3319667645
Total Pages : 335 pages
Book Rating : 4.3/5 (196 download)
Download or read book Mathematics for Nonlinear Phenomena — Analysis and Computation written by Yasunori Maekawa and published by Springer. This book was released on 2017-11-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.
Author : Man Chun Li
Publisher : Stanford University
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.F/5 ( download)
Download or read book On a Free Boundary Problem for Embedded Minimal Surfaces and Instability Theorems for Manifolds with Positive Isotropic Curvature written by Man Chun Li and published by Stanford University. This book was released on 2011 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we describe a min-max construction of embedded minimal surfaces satisfying the free boundary condition in any compact 3-manifolds with boundary. We also prove the instability of minimal surfaces of certain conformal type in 4- manifolds with positive isotropic curvature. Given a compact 3-manifold M with boundary [d̳]M, consider the problem of find- ing an embedded minimal surface [Sigma] which meets [d̳]M orthogonally along [d̳][Sigma]. These surfaces are critical points to the area functional with respect to variations preserving [delta]M. We will use a min-max construction to construct such a free boundary solution and prove the regularity of such solution up to the free boundary. An interesting point is that no convexity assumption on [d̳]M is required. We also discuss some geometric properties, genus bounds for example, for these free boundary solutions. Just as positive sectional curvature tends to make geodesics unstable, positive isotropic curvature tends to make minimal surfaces unstable. In the second part of this thesis, we prove a similar instability result in dimension 4. Given a compact 4- manifold M with positive isotropic curvature, we show that any complete immersed minimal surface [Sigma] in M which is uniformly conformally equivalent to the complex plane is unstable. The same conclusion holds in higher dimensions as well if we assume that the manifold has uniformly positive complex sectional curvature. The proof uses the H ̈ormander's weighted L^2 method and the stability inequality to derive a contradiction.
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 : 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 : Shing-Tung Yau
Publisher :
ISBN 13 :
Total Pages : 460 pages
Book Rating : 4.3/5 (91 download)
Download or read book Surveys in Differential Geometry written by Shing-Tung Yau and published by . This book was released on 2003 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sungbok Hong
Publisher : Springer
ISBN 13 : 364231564X
Total Pages : 163 pages
Book Rating : 4.6/5 (423 download)
Download or read book Diffeomorphisms of Elliptic 3-Manifolds written by Sungbok Hong and published by Springer. This book was released on 2012-08-29 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background
Author : Ignace Van De Woestyne
Publisher : World Scientific
ISBN 13 : 9814547514
Total Pages : 426 pages
Book Rating : 4.8/5 (145 download)
Download or read book Geometry And Topology Of Submanifolds Viii written by Ignace Van De Woestyne and published by World Scientific. This book was released on 1996-10-25 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings consists of papers presented at the international meeting of Differential Geometry and Computer Vision held in Norway and of international meetings on Pure and Applied Differential Geometry held in Belgium. This volume is dedicated to Prof Dr Tom Willmore for his contribution to the development of the domain of differential geometry. Furthermore, it contains a survey on recent developments on affine differential geometry, including a list of publications and a problem list.
Author : Australian Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 388 pages
Book Rating : 4.3/5 (91 download)
Download or read book Gazette - Australian Mathematical Society written by Australian Mathematical Society and published by . This book was released on 1987 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
