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Geometry and Analysis(Vol.II)(几何与分析)(第II卷)


作者:
季理真
定价:
88.00元
ISBN:
978-7-04-030661-3
版面字数:
800.000千字
开本:
16开
全书页数:
563页
装帧形式:
精装
重点项目:
暂无
出版时间:
2010-10-08
读者对象:
学术著作
一级分类:
自然科学
二级分类:
数学与统计
三级分类:
几何分析

The launch of this Advanced Lectures in Mathematics series is aimedat keeping mathematicians informed of the latest developments inmathematics, as well as toaid in the learning of new mathematicaltopics by students all over the world. Each volume consists ofeither an expository monograph or a collection of signify cantintroductions to important topics, This series emphasizes thehistory and sources of motivation for the topics under discussion,and also gives an overview of the current status of research ineach particular field. These volumes are the first source to whichpeople will turn in order to learn new subjects and to dis coverthe latest results of many cutting-edge fields inmathematics.

This book contains many substantial papers from distinguishedspeakers of a conference 'Geometric Analysis: Present and Future'and an overview of the works of Professor Shing-Tung Yau.Contributors include E. Witten, Y.T. Siu, R. Hamilton, H. Hitchin,B. Lawson, A. Strominger, C. Vafa, W. Schmid, V. Guillemin, N. Mok,D. Christodoulou. This is a valuable reference that gives anup-to-dated summary of geometric analysis and its applications inmany different areas of mathematics.

  • Front Matter
  • Part 3 Mathematical Physics, Algebraic Geometry and Other Topics
  • The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties
    • Bohan Fang, Chiu-Chu Melissa Liu, David Treumann and Eric Zaslow
    • 1 Introduction
    • 2 Mirror symmetry for toric manifolds
    • 3 T-duality
    • 4 Microlocalization
    • 5 Coherent-constructible correspondence
    • 6 Examples
    • References
  • Superspace: a Comfortably Vast Algebraic Variety
    • T. Hubsch
    • 1 Introduction
    • 2 Off-shell worldline supermultiplets
    • 3 Superspace, by construction
    • 4 The comfortably vast superspace
    • References
  • A Report on the Yau-Zaslow Formula
    • Naichung Conan Leung
    • 1 Yau-Zaslow formula and its generalizations
    • 2 Yau-Zaslow approach
    • 3 Matching method
    • 4 Degeneration method
    • 5 Calabi-Yau threefold method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
    • 6 Conclusions
    • References
  • Hermitian-Yang-Mills Connections on Kahler Manifolds
    • Jun Li
    • 1 Introduction
    • 2 Donaldson-Uhlenbeck-Yau theorem
    • 3 Hermitian-Yang-Mills connections on curves
    • 4 Hermitian-Yang-Mills connections on surfaces
    • 5 HYM connections on high dimensional varieties
    • 6 Concluding remark
    • References
  • Additivity and Relative Kodaira Dimensions
    • Tian-Jun Li and Weiyi Zhang
    • 1 Introduction
    • 2 Kodaira Dimensions and ber bundles
    • 3 Embedded symplectic surfaces and relative Kod. dim. in dim. 4
    • 4 Relative Kod. dim. in dim. 2 and brations over a surface
    • References
  • Descendent Integrals and Tautological Rings of Moduli Spaces of Curves
    • Kefeng Liu and Hao Xu
    • 1 Introduction
    • 2 Intersection numbers and the Witten-Kontsevich theorem
    • 3 The n-point function
    • 4 Hodge integrals
    • 5 Higher Weil-Petersson volumes
    • 6 Faber’s conjecture on tautological rings
    • 7 Dimension of tautological rings
    • 8 Gromov-Witten invariants
    • 9 Witten’s r-spin numbers
    • References
  • A General Voronoi Summation Formula for GL(n
    • Stephen D. Miller and Wilfried Schmid
    • 1 Introduction
    • 2 Automorphic Distributions
    • 3 Vanishing to in nite order
    • 4 Classical proof of the formula
    • 5 Adelic proof of the formula
    • References
  • Geometry of Holomorphic Isometries and Related Maps between Bounded Domains
    • Ngaiming Mok
    • 1 Examples of holomorphic isometries
    • 2 Analytic continuation of germs of holomorphic isometries
    • 3 Holomorphic isometries of the Poincar e disk into bounded symmetric domains
    • 4 Measure-preserving algebraic correspondences on irreducible bounded symmetric domains
    • 5 Open problems
    • References
  • Abundance Conjecture
    • Yum-Tong Siu
    • 0 Introduction
    • 1 Curvature current and dichotomy
    • 2 Gelfond-Schneider’s technique of algebraic values of solutions of algebraically de ned di erential equations
    • 3 Final step of the case of zero numerical Kodaira dimension
    • 4 Numerically trivial foliations and brations for canonical line bundle
    • 5 Curvature of zeroth direct image of relative canonical and pluricanonical bundle
    • 6 Strict positivity of direct image of relative pluricanonical bundle along numerically trivial bers in the base of numerically trivial bration
    • 7 Technique of Nevanlinna’s rst main theorem for proof of compactness of leaves of foliation
    • References
  • Sasaki-Einstein Geometry
    • James Sparks
    • 1 Sasakian geometry
    • 2 Constructions of Sasaki-Einstein manifolds
    • 3 Obstructions
    • 4 Sasaki-Einstein manifolds in string theory
    • References
  • A Simple Proof of the Chiral Gravity Conjecture
    • Andrew Strominger
  • Geometry of Grand Uni cation
    • Cumrun Vafa
    • 1 Introduction
    • 2 Standard model and gauge symmetry breaking
    • 3 Flavors and hierarchy
    • 4 Uni cation of gauge groups
    • 5 String theory, forces, matter, and interactions
    • 6 F-theory vacua
    • 7 Applications to particle physics
    • 8 Further issues
    • References
  • Quantum Invariance Under Flop Transitions
    • Chin-Lung Wang
    • 1 Introduction
    • ops: Genus zero theory
    • 3 Calabi-Yau ops
    • References
  • The Problem Of Gauge Theory
    • Edward Witten
    • 1 Yang-Mills equations
    • 2 Classical phase space
    • 3 Quantization
    • 4 Nonperturbative approach
    • 5 Breaking of conformal invariance and the mass gap
    • References
  • Part 4 Appendices
  • Shing-Tung Yau, a Manifold Man of Mathematics
    • Lizhen Ji and Kefeng Liu
    • 1 Childhood and early school education
    • 2 Middle school and college
    • 3 Graduate school
    • 4 Professional career
    • 5 Major contributions to mathematics
    • 6 Visits to China
    • 7 Research centers and mathematics institutes
    • 8 ICCM
    • 9 Conferences and popular mathematics programs
    • 10 Mathematics and Chinese literature
    • 11 Family, friends and students
    • 12 Summary
    • References
  • Perspectives on Geometric Analysis
    • Shing-Tung Yau
    • 1 History and contributors of the subject
    • 2 Construction of functions in geometry
    • 3 Mappings between manifolds and rigidity of geometric structures
    • 4 Submanifolds de ned by variational principles
    • 5 Construction of geometric structures on bundles and manifolds
    • References
  • A Survey of Calabi-Yau Manifolds
    • Shing-Tung Yau
    • 1 Introduction
    • 2 General Constructions of Complete Ricci-Flat Metrics in Kahler Geometry
    • 3 Moduli and Arithmetic of Calabi-Yau Manifolds
    • 4 Calabi-Yau Manifolds in Physics
    • 5 Invariants of Calabi-Yau Manifolds
    • 6 Homological Mirror Symmetry
    • 7 SYZ geometric interpretation of mirror symmetry
    • 8 Geometries Related to Calabi-Yau Manifolds
    • References
  • 版权
  • 彩图

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