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| Author | : Société mathématique de France. Journées |
| Publisher | : |
| Total Pages | : 94 |
| Release | : 1993 |
| Genre | : Calculus of variations |
| ISBN | : |
| Author | : Frank Morgan |
| Publisher | : Academic Press |
| Total Pages | : 259 |
| Release | : 2008-09-09 |
| Genre | : Mathematics |
| ISBN | : 0080922406 |
Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers. This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincaré Conjecture. This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject. New to the 4th edition: * Abundant illustrations, examples, exercises, and solutions. * The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori." * A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture." * Contributions by undergraduates.
| Author | : Denis Weaire |
| Publisher | : CRC Press |
| Total Pages | : 190 |
| Release | : 1997-09-09 |
| Genre | : Science |
| ISBN | : 9780748406326 |
In 1887, Kelvin posed one of the most discussed scientific questions of the last 100 years - the problem of the division of three-dimensional space into cells of equal volume with minimal area. It has interested mathematicians, physical scientists and biologists ever since and the problem has scientific relevance to foams, emulsions and many other kinds of cells. In the 1990s, a more complex structure was discovered by Robert Phelan and Denis Weaire and it remains the best yet found. This text assesses the various merits of Kelvin's structure and of that discovered by Weaire and Phelan. It also looks at the problem of proof that Weaire's structure having minimal area remains open.
| Author | : Ivan Charles Sterling |
| Publisher | : |
| Total Pages | : 82 |
| Release | : 1985 |
| Genre | : |
| ISBN | : |
| Author | : Steven James Cox |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 169 |
| Release | : 2004 |
| Genre | : Computers |
| ISBN | : 0821837206 |
The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems whose most natural solution occurs by differentiating a one-parameter family of variations of some function. The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.
| Author | : Frederick J. Almgren |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 638 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780821810675 |
This volume offers a unique collection of some of the work of Frederick J. Almgren, Jr., the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. Included in the volume are the following: a summary by Sheldon Chang of the famous 1700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $Rn$, a detailed summary by Brian White of Almgren's contributions to mathematics, his own announcements of several longer papers, important shorter papers, and memorable expository papers. Almgren's enthusiasm for the subject and his ability to locate mathematically beautiful problems that were "ready to be solved" attracted many students who further expanded the subject into new areas. Many of these former students are now known for the clarity of their expositions and for the beauty of the problems that they work on. As Almgren's former graduate student, wife, and colleague, Professor Taylor has compiled an important volume on an extraordinary mathematician. This collection presents a fine comprehensive view of the man's mathematical legacy
| Author | : Frank Morgan |
| Publisher | : Elsevier |
| Total Pages | : 154 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483277801 |
Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.
| Author | : Manuel Ritoré |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 113 |
| Release | : 2009-10-19 |
| Genre | : Mathematics |
| ISBN | : 303460212X |
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 | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2004 |
| Genre | : |
| ISBN | : |
| Author | : Takeshi Kotake |
| Publisher | : |
| Total Pages | : 518 |
| Release | : 1993 |
| Genre | : Gauge fields (Physics) |
| ISBN | : |
