Surfaces with Constant Mean Curvature

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821834794
Total Pages : 156 pages
Book Rating : 4.8/5 (347 download)

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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.

A Course in Minimal Surfaces

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Author :
Publisher : American Mathematical Society
ISBN 13 : 1470476401
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Course in Minimal Surfaces by : Tobias Holck Colding

Download or read book A Course in Minimal Surfaces written by Tobias Holck Colding and published by American Mathematical Society. This book was released on 2024-01-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 796 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on K3 Surfaces

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Publisher : Cambridge University Press
ISBN 13 : 1316797252
Total Pages : 499 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Mostly Surfaces

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Publisher : American Mathematical Soc.
ISBN 13 : 0821853686
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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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.

Arnold's Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540206149
Total Pages : 664 pages
Book Rating : 4.2/5 (61 download)

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Book Synopsis Arnold's Problems by : Vladimir I. Arnold

Download or read book Arnold's Problems written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2004-06-24 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

Journal of the Mathematical Society of Japan

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Publisher :
ISBN 13 :
Total Pages : 504 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Journal of the Mathematical Society of Japan by : Nihon Sūgakkai

Download or read book Journal of the Mathematical Society of Japan written by Nihon Sūgakkai and published by . This book was released on 2000 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Regularization and Partial Regularity for Motion by Mean Curvature

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821825828
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Elliptic Regularization and Partial Regularity for Motion by Mean Curvature by : Tom Ilmanen

Download or read book Elliptic Regularization and Partial Regularity for Motion by Mean Curvature written by Tom Ilmanen and published by American Mathematical Soc.. This book was released on 1994 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study Brakke's motion of varifolds by mean curvature in the special case that the initial surface is an integral cycle, giving a new existence proof by mean of elliptic regularization. Under a uniqueness hypothesis, we obtain a weakly continuous family of currents solving Brakke's motion. These currents remain within the corresponding level-set motion by mean curvature, as defined by Evans-Spruck and Chen-Giga-Goto. Now let [italic capital]T0 be the reduced boundary of a bounded set of finite perimeter in [italic capital]R[superscript italic]n. If the level-set motion of the support of [italic capital]T0 does not develop positive Lebesgue measure, then there corresponds a unique integral [italic]n-current [italic capital]T, [partial derivative/boundary/degree of a polynomial symbol][italic capital]T = [italic capital]T0, whose time-slices form a unit density Brakke motion. Using Brakke's regularity theorem, spt [italic capital]T is smooth [script capital]H[superscript italic]n-almost everywhere. In consequence, almost every level-set of the level-set flow is smooth [script capital]H[superscript italic]n-almost everywhere in space-time.

The Giant Vesicle Book

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Publisher : CRC Press
ISBN 13 : 1498752187
Total Pages : 652 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Giant Vesicle Book by : Rumiana Dimova

Download or read book The Giant Vesicle Book written by Rumiana Dimova and published by CRC Press. This book was released on 2019-11-19 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giant vesicles are widely used as a model membrane system, both for basic biological systems and for their promising applications in the development of smart materials and cell mimetics, as well as in driving new technologies in synthetic biology and for the cosmetics and pharmaceutical industry. The reader is guided to use giant vesicles, from the formation of simple membrane platforms to advanced membrane and cell system models. It also includes fundamentals for understanding lipid or polymer membrane structure, properties and behavior. Every chapter includes ideas for further applications and discussions on the implications of the observed phenomena towards understanding membrane-related processes. The Giant Vesicle Book is meant to be a road companion, a trusted guide for those making their first steps in this field as well as a source of information required by experts. Key Features • A complete summary of the field, covering fundamental concepts, practical methods, core theory, and the most promising applications • A start-up package of theoretical and experimental information for newcomers in the field • Extensive protocols for establishing the required preparations and assays • Tips and instructions for carefully performing and interpreting measurements with giant vesicles or for observing them, including pitfalls • Approaches developed for investigating giant vesicles as well as brief overviews of previous studies implementing the described techniques • Handy tables with data and structures for ready reference

Differential Geometry of Curves and Surfaces

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Publisher : Springer Science & Business Media
ISBN 13 : 0817644024
Total Pages : 215 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Differential Geometry of Curves and Surfaces by : Victor Andreevich Toponogov

Download or read book Differential Geometry of Curves and Surfaces written by Victor Andreevich Toponogov and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

Physics Briefs

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Publisher :
ISBN 13 :
Total Pages : 1108 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Physics Briefs by :

Download or read book Physics Briefs written by and published by . This book was released on 1992 with total page 1108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Foliations and the Geometry of 3-Manifolds

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Publisher : Oxford University Press on Demand
ISBN 13 : 0198570082
Total Pages : 378 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari

Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Nature

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Publisher :
ISBN 13 :
Total Pages : 670 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Nature by : Sir Norman Lockyer

Download or read book Nature written by Sir Norman Lockyer and published by . This book was released on 1887 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sources of Gravitational Radiation

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Publisher : CUP Archive
ISBN 13 : 9780521227780
Total Pages : 536 pages
Book Rating : 4.2/5 (277 download)

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Book Synopsis Sources of Gravitational Radiation by : Larry L. Smarr

Download or read book Sources of Gravitational Radiation written by Larry L. Smarr and published by CUP Archive. This book was released on 1979-09-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nilpotence and Periodicity in Stable Homotopy Theory

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Publisher : Princeton University Press
ISBN 13 : 9780691025728
Total Pages : 228 pages
Book Rating : 4.0/5 (257 download)

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Book Synopsis Nilpotence and Periodicity in Stable Homotopy Theory by : Douglas C. Ravenel

Download or read book Nilpotence and Periodicity in Stable Homotopy Theory written by Douglas C. Ravenel and published by Princeton University Press. This book was released on 1992-11-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.

Differential Geometry of Complex Vector Bundles

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Publisher : Princeton University Press
ISBN 13 : 1400858682
Total Pages : 317 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Differential Geometry of Complex Vector Bundles by : Shoshichi Kobayashi

Download or read book Differential Geometry of Complex Vector Bundles written by Shoshichi Kobayashi and published by Princeton University Press. This book was released on 2014-07-14 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Nature

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Publisher :
ISBN 13 :
Total Pages : 872 pages
Book Rating : 4.B/5 (1 download)

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Book Synopsis Nature by :

Download or read book Nature written by and published by . This book was released on 1887 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: