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Author: Magdalena D. Toda
Publisher: CRC Press
ISBN: 1498744648
Category : Mathematics
Languages : en
Pages : 157
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Book Description
This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry. Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces? As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area.
Author: Magdalena D. Toda
Publisher: CRC Press
ISBN: 1498744648
Category : Mathematics
Languages : en
Pages : 157
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Book Description
This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry. Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces? As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area.
Author: Magdalena Toda
Publisher:
ISBN: 9781315151830
Category : MATHEMATICS
Languages : en
Pages : 141
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Book Description
"This book is the first monograph dedicated entirely to Willmore energy and Willmore surfaces as contemporary topics in differential geometry. While it focuses on Willmore energy and related conjectures, it also sits at the intersection between integrable systems, harmonic maps, Lie groups, calculus of variations, geometric analysis and applied differential geometry. Rather than reproducing published results, it presents new directions, developments and open problems. It addresses questions like: What is new in Willmore theory? Are there any new Willmore conjectures and open problems? What are the contemporary applications of Willmore surfaces?As well as mathematicians and physicists, this book is a useful tool for postdoctoral researchers and advanced graduate students working in this area. "--Provided by publisher.
Author: Giuseppe Mingione
Publisher: Springer Science & Business Media
ISBN: 887642427X
Category : Mathematics
Languages : en
Pages : 211
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Book Description
This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.
Author: Áurea Casinhas Quintino
Publisher: Cambridge University Press
ISBN: 1108794424
Category : Mathematics
Languages : en
Pages : 261
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Book Description
From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.
Author: Hubert L. Bray
Publisher: American Mathematical Soc.
ISBN: 1470423138
Category : Geometric analysis
Languages : en
Pages : 456
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Book Description
This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace–Beltrami operators.
Author: Tim Hoffmann
Publisher: Springer Nature
ISBN: 3030685411
Category : Mathematics
Languages : en
Pages : 280
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Book Description
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.
Author: Jimmy Petean
Publisher: American Mathematical Soc.
ISBN: 1470423103
Category : Mathematics
Languages : en
Pages : 201
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Book Description
This volume contains the proceedings of the First Mathematical Congress of the Americas, held from August 5-9, 2013, in Guanajuato, México. With the participation of close to 1,000 researchers from more than 40 countries, the meeting set a benchmark for mathematics in the two continents. The papers, written by some of the plenary and invited speakers, as well as winners of MCA awards, cover new developments in classic topics such as Hopf fibrations, minimal surfaces, and Markov processes, and provide recent insights on combinatorics and geometry, isospectral spherical space forms, homogenization on manifolds, and Lagrangian cobordism, as well as applications to physics and biology.
Author: Frank Morgan
Publisher: Academic Press
ISBN: 0128045272
Category : Mathematics
Languages : en
Pages : 272
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Book Description
Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe. The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers. Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications. Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures Enables further study of more advanced topics and texts Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques Contains full topical coverage of The Log-Convex Density Conjecture Comprehensively updated throughout
Author: Udo Hertrich-Jeromin
Publisher: Cambridge University Press
ISBN: 9780521535694
Category : Mathematics
Languages : en
Pages : 436
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Book Description
This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.
Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821890431
Category : Science
Languages : en
Pages : 108
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Book Description
Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.
