Minimal Surfaces Geometric Analysis And Symplectic Geometry

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Minimal Surfaces Geometric Analysis And Symplectic Geometry

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Author : Kenji Fukaya
language : en
Publisher:
Release Date : 2002

Minimal Surfaces Geometric Analysis And Symplectic Geometry written by Kenji Fukaya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The 1998-1999 programme year of the Japan-U.S. Mathematics Institute at the Johns Hopkins University, USA was devoted to minimal surfaces, geometric analysis, and symplectic geometry. The programme culminated in a week-long workshop and conference to discuss developments. This volume is a collection of articles written by the speakers. It presents extended or modified versions of the lectures delivered at the meeting. Each article provides a vivid account of contemporary research, with the information given ranging from introductory level to the most up-to-date results. Of special interest is a long survey article by K. Fukaya on applications of Floer homology to mirror symmetry. Also discussed are developments on the geometry of constant mean curvature one surfaces in hyperbolic 3-spaces of finite total curvature. The range of topics covered in the volume provides direction for further research in these rapidly developing areas. The book should be suitable for graduate students and researchers interested in differential and symplectic geometry.

Symplectic Poisson And Noncommutative Geometry

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Author : Tohru Eguchi
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-25

Symplectic Poisson And Noncommutative Geometry written by Tohru Eguchi 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 2014-08-25 with Mathematics categories.

This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute.

Lagrangian Intersection Floer Theory

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Author : Kenji Fukaya
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-06-21

Lagrangian Intersection Floer Theory written by Kenji Fukaya 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 2010-06-21 with Mathematics categories.

This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Lectures On Symplectic Geometry

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Author : Ana Cannas da Silva
language : en
Publisher: Springer
Release Date : 2004-10-27

Lectures On Symplectic Geometry written by Ana Cannas da Silva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-27 with Mathematics categories.

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Geometric Relativity

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Author : Dan A. Lee
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-20

Geometric Relativity written by Dan A. Lee and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-20 with Mathematics categories.

Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the first time these topics have been gathered into a single place and presented with an advanced graduate student audience in mind; several dozen exercises are also included. The main prerequisite for this book is a working understanding of Riemannian geometry and basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.

Fukaya Categories And Picard Lefschetz Theory

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Author : Paul Seidel
language : en
Publisher: European Mathematical Society
Release Date : 2008

Fukaya Categories And Picard Lefschetz Theory written by Paul Seidel and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

Constant Mean Curvature Surfaces With Boundary

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Author : Rafael López
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-31

Constant Mean Curvature Surfaces With Boundary written by Rafael López 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 2013-08-31 with Mathematics categories.

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.

Momentum Maps And Hamiltonian Reduction

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Author : Juan-Pablo Ortega
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Momentum Maps And Hamiltonian Reduction written by Juan-Pablo Ortega 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 2013-04-17 with Mathematics categories.

The use of the symmetries of a physical system in the study of its dynamics has a long history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques are often implemented by using the integrals 01 motion that one can sometimes associate to these symmetries. The integrals of motion of a dynamical system are quan tities that are conserved along the fiow of that system. In c1assieal mechanics symme tries are usually induced by point transformations, that is, they come exc1usively from symmetries of the configuration space; the intimate connection between integrals of motion and symmetries was formalized in this context by NOETHER (1918). This idea can be generalized to many symmetries of the entire phase space of a given system, by associating to the Lie algebra action encoding the symmetry, a function from the phase space to the dual of the Lie algebra. This map, whose level sets are preserved by the dynamics of any symmetrie system, is referred to in modern terms as a momentum map of the symmetry, a construction already present in the work of LIE (1890). Its remarkable properties were rediscovered by KOSTANT (1965) and SOURlAU (1966, 1969) in the general case and by SMALE (1970) for the lifted action to the co tangent bundle of a configuration space. For the his tory of the momentum map we refer to WEINSTEIN (1983b) and MARSDEN AND RATIU (1999), §11. 2.

Noncommutative Homological Mirror Functor

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Author : Cheol-Hyun Cho
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24

Noncommutative Homological Mirror Functor written by Cheol-Hyun Cho and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Mathematics categories.

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Riemannian Geometry And Geometric Analysis

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Author : Jürgen Jost
language : en
Publisher: Springer
Release Date : 2017-10-13

Riemannian Geometry And Geometric Analysis written by Jürgen Jost and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-13 with Mathematics categories.

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik