Constrained Willmore Surfaces
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Constrained Willmore Surfaces
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Author : Áurea Casinhas Quintino
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-10
Constrained Willmore Surfaces written by Áurea Casinhas Quintino and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-10 with Mathematics categories.
From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.
Willmore Energy And Willmore Conjecture
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Author : Magdalena D. Toda
language : en
Publisher: CRC Press
Release Date : 2017-10-30
Willmore Energy And Willmore Conjecture written by Magdalena D. Toda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with Mathematics categories.
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.
Minimal Surfaces Integrable Systems And Visualisation
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Author : Tim Hoffmann
language : en
Publisher: Springer Nature
Release Date : 2021-05-06
Minimal Surfaces Integrable Systems And Visualisation written by Tim Hoffmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.
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.
Constrained Willmore Surfaces
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Author : Aurea Casinhas Quintino
language : en
Publisher:
Release Date : 2008
Constrained Willmore Surfaces written by Aurea Casinhas Quintino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Differential Geometry And Integrable Systems
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Author : Martin A. Guest
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Differential Geometry And Integrable Systems written by Martin A. Guest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced byintegrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generallyreveals previously unnoticed symmetries and can lead to surprisingly explicit solutions. Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and willserve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The second volume from this conference also available from the AMS is Integrable Systems,Topology, and Physics, Volume 309 CONM/309in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.
Harmonic Maps And Differential Geometry
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Author : Eric Loubeau
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Harmonic Maps And Differential Geometry written by Eric Loubeau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.
Symposium On The Differential Geometry Of Submanifolds
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Author : Luc Vrancken
language : en
Publisher: Lulu.com
Release Date : 2008-06-30
Symposium On The Differential Geometry Of Submanifolds written by Luc Vrancken and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-30 with Mathematics categories.
This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian immersions, Minimal immersions and constant mean curvature immersions, Harmonic maps and harmonic morphisms, Variational problems, Affine differential geometry. This conference follows the tradition of the conferences in the series of « Geometry and Topology of Submanifolds », which started with the Luminy meeting in 1987 and then continued with various meetings at different places in Europe, such as amongst others Avignon, Leeds, Leuven, Brussels, Nordfjordeid, Berlin, Warszawa, Bedlewo and also in China (Beijing, 1998).
Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems
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Author : Johannes C. C. Nitsche
language : en
Publisher:
Release Date : 1989
Lectures On Minimal Surfaces Introduction Fundamentals Geometry And Basic Boundary Value Problems written by Johannes C. C. Nitsche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This book is a revised and translated version of the first five chapters of Vorlesungen ^D"uber Minimalfl^D"achen. It deals with the parametric minimal surface in Euclidean space. The author presents a broad survey that extends from the classical beginnings to the current situation while highlighting many of the subject's main features and interspersing the mathematical development with pertinent historical remarks.
Conformal Maps Of A Riemannian Surface Into The Space Of Quaternions
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Author : Dr. Jörg Richter
language : en
Publisher:
Release Date : 1997-09-01
Conformal Maps Of A Riemannian Surface Into The Space Of Quaternions written by Dr. Jörg Richter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-01 with Mathematics categories.
In the present work, a coordinate-free way is suggested to handle conformal maps of a Riemannian surface into a space of constant curvature of maximum dimension 4, modeled on the non-commutative field of quaternions. This setup for the target space and the idea to treat differential 2-forms on Riemannian surfaces as quadratic functions on the tangent space, are the starting points for the development of the theory of conformal maps and in particular of conformal immersions. As a first result, very nice conditions for the conformality of immersions into 3- and 4-dimensional space-forms are deduced and a simple way to write the second fundamental form is found. If the target space is euclidean 3-space, an alternative approach is proposed by fixing a spin structure on the Riemannian surface. The problem of finding a local immersion is then reduced to that of solving a linear Dirac equation with a potential whose square is the Willmore integrand. This allows to make statements about the structure of the moduli space of conformal immersions and to derive a very nice criterion for a conformal immersion to be constrained Willmore. As an application the Dirac equation with constant potential over spheres and tori is solved. This yields explicit immersion formulae out of which there were produced pictures, the Dirac-spheres and -tori. These immersions have the property that their Willmore integrand generates a metric of vanishing and constant curvature, respectively. As a next step an affine immersion theory is developped. This means, one starts with a given conformal immersion into euclidean 3-space and looks for new ones in the same conformal class. This is called a spin-transformation and it leads one to solve an affine Dirac equation. Also, it is shown how the coordinate-dependent generalized Weierstrass representation fits into the present framework. In particular, it is now natural to consider the class of conformal immersions that admit new conformal immersions having the same potential. It turns out, that all geometrically interesting immersions admit such an isopotential spin-transformation and that this property of an immersion is even a conformal invariant of the ambient space. It is shown that conformal isothermal immersions generate both via their dual and via Darboux transformations non-trivial families of new isopotential conformal immersions. Similarly to this, conformal (constrained) Willmore immersions produce non-trivial families of isopotential immersions of which subfamilies are (constrained) Willmore again having even the same Willmore integral. Another observation is, that the Euler-Lagrange equation for the Willmore problem is the integrability condition for a quaternionic 1-form, which generates a conformal minimal immersions into hyperbolic 4-space. Vice versa, any such immersion determines a conformal Willmore immersion. As a consequence, there is a one-to-one correspondence between conformal minimal immersions into Lorentzian space and those into hyperbolic space, which generalizes to any dimension. There is also induced an action on conformal minimal immersions into hyperbolic 4-space. Another fact is, that conformal constant mean curvature (cmc) immersions into some 3-dimensional space form unveil to be isothermal and constrained Willmore. The reverse statement is true at least for tori. Finally a very simple proof of a theorem by R.Bryant concerning Willmore spheres is given. In the last part, time-dependent conformal immersions are considered. Their deformation formulae are computed and it is investigated under what conditions the flow commutes with Moebius transformations. The modified Novikov-Veselov flow is written down in a conformal invariant way and explicit deformation formulae for the immersion function itself and all of its invariants are given. This flow commutes with Moebius transformations. Its definition is coupled with a delta-bar problem, for which a solution is presented under special conditions. These are fulfilled at least by cmc immersions and by surfaces of revolution and the general flow formulae reduce to very nice formulae in these cases.
From Geometry To Quantum Mechanics
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Author : Yoshiaki Maeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-22
From Geometry To Quantum Mechanics written by Yoshiaki Maeda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-22 with Mathematics categories.
* Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference