Infinite Dimensional K Hler Manifolds

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Riemannian Topology And Geometric Structures On Manifolds

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Author : Krzysztof Galicki
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-25

Riemannian Topology And Geometric Structures On Manifolds written by Krzysztof Galicki 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 2010-07-25 with Mathematics categories.

Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.

Classical Mirror Symmetry

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Author : Masao Jinzenji
language : en
Publisher: Springer
Release Date : 2018-04-18

Classical Mirror Symmetry written by Masao Jinzenji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-18 with Science categories.

This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold.First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold.On the B-model side, the process of construction of a pair of mirror Calabi–Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard–Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis.On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given.The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.

Stochastic Pdes And Modelling Of Multiscale Complex System

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Author : Xiaopeng Chen
language : en
Publisher: World Scientific
Release Date : 2019-05-07

Stochastic Pdes And Modelling Of Multiscale Complex System written by Xiaopeng Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

An Introduction To Extremal Kahler Metrics

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Author : Gábor Székelyhidi
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-19

An Introduction To Extremal Kahler Metrics written by Gábor Székelyhidi 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 2014-06-19 with Mathematics categories.

A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Analysis And Geometry On Graphs And Manifolds

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Author : Matthias Keller
language : en
Publisher: Cambridge University Press
Release Date : 2020-08-20

Analysis And Geometry On Graphs And Manifolds written by Matthias Keller 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 2020-08-20 with Mathematics categories.

A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.

Surveys In Differential Geometry

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Author : Huai-Dong Cao
language : en
Publisher:
Release Date : 2009

Surveys In Differential Geometry written by Huai-Dong Cao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

Physics Briefs

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Author :
language : en
Publisher:
Release Date : 1981

Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Physics categories.

Northern California Symplectic Geometry Seminar

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Author : Y. Eliashberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Northern California Symplectic Geometry Seminar written by Y. Eliashberg 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 1999 with Mathematics categories.

The 12 papers are from various meeting of the seminar, which has met regularly since 1989. They discuss the quantization of symplectic orbitfolds and group actions; Hamiltonian dynamical systems without period orbits; the stabilization of symplectic inequalities and applications; Engel deformations and contact structures; quantum products for mapping tori and the Atiya-Floer conjecture; the cohomology rings of Hamiltonian T-spaces; symmetric spaces, Kahler geometry, and Hamiltonian dynamics; the mirror formula for quintic threefolds; the virtual moduli cycle; Floer homology, Novikov rings, and complete intersections; surgery, quantum cohomology, and birational geometry; and group symplectic automorphisms. They are not indexed. Annotation copyrighted by Book News, Inc., Portland, OR.

Complex Monge Amp Re Equations And Geodesics In The Space Of K Hler Metrics

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Author : Vincent Guedj
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-06

Complex Monge Amp Re Equations And Geodesics In The Space Of K Hler Metrics written by Vincent Guedj 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 2012-01-06 with Mathematics categories.

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Infinite Dimensional Kahler Manifolds

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Author : Alan Huckleberry
language : en
Publisher:
Release Date : 2001-09-01

Infinite Dimensional Kahler Manifolds written by Alan Huckleberry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-01 with categories.