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Author : H. Blaine Lawson
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.3/5 (91 download)
Download or read book Lectures on Minimal Submanifolds written by H. Blaine Lawson and published by . This book was released on 1980 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Anciaux
Publisher : World Scientific
ISBN 13 : 9814291242
Total Pages : 184 pages
Book Rating : 4.8/5 (142 download)
Download or read book Minimal Submanifolds in Pseudo-Riemannian Geometry written by Henri Anciaux and published by World Scientific. This book was released on 2011 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. For the first time, this textbook provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Khler manifolds are given.
Author : Kichoon Yang
Publisher : Springer Science & Business Media
ISBN 13 : 9780792303992
Total Pages : 198 pages
Book Rating : 4.3/5 (39 download)
Download or read book Complete and Compact Minimal Surfaces written by Kichoon Yang and published by Springer Science & Business Media. This book was released on 1989-09-30 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ... , si j'avait su comment en reveni.r, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non 111e series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author : Enrico Bombieri
Publisher : Princeton University Press
ISBN 13 : 1400881439
Total Pages : 368 pages
Book Rating : 4.4/5 (8 download)
Download or read book Seminar On Minimal Submanifolds. (AM-103), Volume 103 written by Enrico Bombieri and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar On Minimal Submanifolds. (AM-103), Volume 103, will be forthcoming.
Author : Bennett Chow
Publisher : American Mathematical Society
ISBN 13 : 147047767X
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 2024-09-23 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 : Ulrich Dierkes
Publisher : Springer Science & Business Media
ISBN 13 : 3662027917
Total Pages : 528 pages
Book Rating : 4.6/5 (62 download)
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 : Morio Obata
Publisher : North Holland
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.:/5 (44 download)
Download or read book Minimal Submanifolds and Geodesics written by Morio Obata and published by North Holland. This book was released on 1979 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : James Carlson
Publisher : Cambridge University Press
ISBN 13 : 1108118186
Total Pages : 577 pages
Book Rating : 4.1/5 (81 download)
Download or read book Period Mappings and Period Domains written by James Carlson and published by Cambridge University Press. This book was released on 2017-08-11 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether–Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford–Tate groups and their associated domains, the Mumford–Tate varieties and generalizations of Shimura varieties.
Author : Andreas Weber
Publisher : MDPI
ISBN 13 : 3039217305
Total Pages : 160 pages
Book Rating : 4.0/5 (392 download)
Download or read book Computer Algebra in Scientific Computing written by Andreas Weber and published by MDPI. This book was released on 2019-11-04 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.
Author : Spiro Karigiannis
Publisher : Springer Nature
ISBN 13 : 1071605771
Total Pages : 392 pages
Book Rating : 4.0/5 (716 download)
Download or read book Lectures and Surveys on G2-Manifolds and Related Topics written by Spiro Karigiannis and published by Springer Nature. This book was released on 2020-05-26 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.
Author : Franki Dillen
Publisher : World Scientific
ISBN 13 : 9814554626
Total Pages : 298 pages
Book Rating : 4.8/5 (145 download)
Download or read book Geometry And Topology Of Submanifolds Iv - Proceedings Of The Conference On Differential Geometry And Vision written by Franki Dillen and published by World Scientific. This book was released on 1992-07-17 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings on pure and applied differential geometry, discusses several subjects in submanifold theory, such as the Willmore problem, minimal surfaces, submanifolds of finite type, affine differential geometry, indefinite Riemannian geometry, and applications of differential geometry in human and artificial vision.
Author : Jean-Luc Brylinski
Publisher : Springer Science & Business Media
ISBN 13 : 0817647317
Total Pages : 318 pages
Book Rating : 4.8/5 (176 download)
Download or read book Loop Spaces, Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2009-12-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Author : Y. L. Xin
Publisher : World Scientific
ISBN 13 : 9812386874
Total Pages : 271 pages
Book Rating : 4.8/5 (123 download)
Download or read book Minimal Submanifolds and Related Topics written by Y. L. Xin and published by World Scientific. This book was released on 2003 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds. This important book presents the Douglas-Rado solution to the Plateau problem, but the main emphasis is on the Bernstein problem and its new developments in various directions: the value distribution of the Gauss image of a minimal surface in Euclidean 3-space, Simons' work for minimal graphic hypersurfaces, and author's own contributions to Bernstein type theorems for higher codimensions. The author also introduces some related topics, such as submanifolds with parallel mean curvature, Weierstrass type representation for surfaces of mean curvature 1 in hyperbolic 3-space, and special Lagrangian submanifolds.
Author : Stancho Dimiev
Publisher : World Scientific
ISBN 13 : 9814479977
Total Pages : 358 pages
Book Rating : 4.8/5 (144 download)
Download or read book Contemporary Aspects Of Complex Analysis, Differential Geometry And Mathematical Physics - Procs Of The 7th Int'l Workshop On Complex Structures And Vector Fields written by Stancho Dimiev and published by World Scientific. This book was released on 2005-07-04 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the cutting-edge contributions to the Seventh International Workshop on Complex Structures and Vector Fields, which was organized as a continuation of the high successful preceding workshops on similar research.The volume includes works treating ambitious topics in differential geometry, mathematical physics and technology such as Bézier curves in space forms, potential and catastrophy of a soap film, computer-assisted studies of logistic maps, and robotics.
Author : Manfredo P. do Carmo
Publisher : Springer Science & Business Media
ISBN 13 : 3642255884
Total Pages : 492 pages
Book Rating : 4.6/5 (422 download)
Download or read book Manfredo P. do Carmo – Selected Papers written by Manfredo P. do Carmo and published by Springer Science & Business Media. This book was released on 2012-04-02 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.
Author : John Oprea
Publisher : American Mathematical Society
ISBN 13 : 1470477912
Total Pages : 497 pages
Book Rating : 4.4/5 (74 download)
Download or read book Differential Geometry and Its Applications written by John Oprea and published by American Mathematical Society. This book was released on 2024-07-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
Author : Henar Herrero
Publisher : Springer Nature
ISBN 13 : 3031620259
Total Pages : 159 pages
Book Rating : 4.0/5 (316 download)
Download or read book Cutting-Edge Mathematics written by Henar Herrero and published by Springer Nature. This book was released on with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
