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Constant Mean Curvature Surfaces In Euclidean And Hyperbolic 3 Space
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Book Synopsis Constant Mean Curvature Surfaces with Boundary by : Rafael López
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.
Book Synopsis Surfaces with Constant Mean Curvature by : Katsuei Kenmotsu
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.
Book Synopsis Encyclopedia of Analytical Surfaces by : S.N. Krivoshapko
Download or read book Encyclopedia of Analytical Surfaces written by S.N. Krivoshapko and published by Springer. This book was released on 2015-02-25 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.
Book Synopsis Painleve Transcendents by : A. S. Fokas
Download or read book Painleve Transcendents written by A. S. Fokas and published by American Mathematical Soc.. This book was released on 2006 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the turn of the twentieth century, the French mathematician Paul Painleve and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painleve I-VI. Although these equations were initially obtainedanswering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painleve transcendents (i.e., the solutionsof the Painleve equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points, play a crucial role in the applications of these functions. It is shown in this book, that even though the six Painleve equations are nonlinear, it is still possible, using a new technique called theRiemann-Hilbert formalism, to obtain analogous explicit formulas for the Painleve transcendents. This striking fact, apparently unknown to Painleve and his contemporaries, is the key ingredient for the remarkable applicability of these ``nonlinear special functions''. The book describes in detail theRiemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painleve functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painleve equations and related areas.
Book Synopsis The Global Theory of Minimal Surfaces in Flat Spaces by : W.H. III Meeks
Download or read book The Global Theory of Minimal Surfaces in Flat Spaces written by W.H. III Meeks and published by Springer. This book was released on 2004-10-11 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
Book Synopsis Isometric Embedding of Riemannian Manifolds in Euclidean Spaces by : Qing Han
Download or read book Isometric Embedding of Riemannian Manifolds in Euclidean Spaces written by Qing Han and published by American Mathematical Soc.. This book was released on 2006 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in ${\mathbb R}^3$. The emphasis is on those PDE techniques which are essential to the most important results of the last century. The classic results in this book include the Janet-Cartan Theorem, Nirenberg's solution of the Weyl problem, and Nash's Embedding Theorem, with a simplified proof by Gunther. The book also includes the main results from the past twenty years, both local and global, on the isometric embedding of surfaces in Euclidean 3-space. The work will be indispensable to researchers in the area. Moreover, the authors integrate the results and techniques into a unified whole, providing a good entry point into the area for advanced graduate students or anyone interested in this subject. The authors avoid what is technically complicated. Background knowledge is kept to an essential minimum: a one-semester course in differential geometry and a one-year course in partial differential equations.
Book Synopsis Visualization and Mathematics by : H.-C. Hege
Download or read book Visualization and Mathematics written by H.-C. Hege and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts. Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.
Book Synopsis The Global Theory of Minimal Surfaces in Flat Spaces by : William Meeks
Download or read book The Global Theory of Minimal Surfaces in Flat Spaces written by William Meeks and published by Springer Science & Business Media. This book was released on 2002-03-25 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
Book Synopsis Noncompact Problems at the Intersection of Geometry, Analysis, and Topology by : Abbas Bahri
Download or read book Noncompact Problems at the Intersection of Geometry, Analysis, and Topology written by Abbas Bahri and published by American Mathematical Soc.. This book was released on 2004 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. Mathematicians attending the conference had interests in noncompact variational problems, pseudo-holomorphic curves, singular and smooth solutions to problems admitting a conformal (or some group) invariance, Sobolev spaces on manifolds, and configuration spaces. One day of the proceedings was devoted to Einstein equations and related topics. Contributors to the volume include, among others, Sun-Yung A. Chang, Luis A. Caffarelli, Carlos E. Kenig, and Gang Tian. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.
Book Synopsis Differential Geometry and Global Analysis by : Bang-Yen Chen
Download or read book Differential Geometry and Global Analysis written by Bang-Yen Chen and published by American Mathematical Society. This book was released on 2022-04-07 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Differential Geometry and Global Analysis, Honoring the Memory of Tadashi Nagano (1930–2017), held January 16, 2020, in Denver, Colorado. Tadashi Nagano was one of the great Japanese differential geometers, whose fundamental and seminal work still attracts much interest today. This volume is inspired by his work and his legacy and, while recalling historical results, presents recent developments in the geometry of symmetric spaces as well as generalizations of symmetric spaces; minimal surfaces and minimal submanifolds; totally geodesic submanifolds and their classification; Riemannian, affine, projective, and conformal connections; the $(M_{+}, M_{-})$ method and its applications; and maximal antipodal subsets. Additionally, the volume features recent achievements related to biharmonic and biconservative hypersurfaces in space forms, the geometry of Laplace operator on Riemannian manifolds, and Chen-Ricci inequalities for Riemannian maps, among other topics that could attract the interest of any scholar working in differential geometry and global analysis on manifolds.
Book Synopsis Minimal Surfaces: Integrable Systems and Visualisation by : Tim Hoffmann
Download or read book Minimal Surfaces: Integrable Systems and Visualisation written by Tim Hoffmann and published by Springer Nature. This book was released on 2021-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and Leicester between 2016 and 2019. Within the theme of the network, the presented articles cover a broad range of topics and explore exciting links between problems related to the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, integrable systems and visualisation. Combining research and overview articles by prominent international researchers, the book offers a valuable resource for both researchers and students who are interested in this research area.
Book Synopsis Geometric Analysis by : Joaqun Prez
Download or read book Geometric Analysis written by Joaqun Prez and published by American Mathematical Soc.. This book was released on 2012-07-16 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry.
Book Synopsis Minimal Submanifolds and Related Topics by : Y. L. Xin
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.
Book Synopsis Séminaire de théorie spectrale et géométrie by :
Download or read book Séminaire de théorie spectrale et géométrie written by and published by . This book was released on 2000 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Differential Geometry, Volume 1 by : F.J.E. Dillen
Download or read book Handbook of Differential Geometry, Volume 1 written by F.J.E. Dillen and published by Elsevier. This book was released on 1999-12-16 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.
Download or read book Global Analysis written by Ilka Agricola and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.
Book Synopsis Mostly Surfaces by : Richard Evan Schwartz
Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
