图书信息
图书目录
极值Kähler度量引论（影印版）
暂无简介
作者：
Gábor Székelyhidi
定价：
99.00元
出版时间：
2023-03-24
ISBN：
978-7-04-059304-4
物料号：
59304-00
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：
分析
重点项目：
暂无
版面字数：
350.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 前辅文
- Chapter 1. K¨ahler Geometry
- 1.1. Complex manifolds
- 1.2. Almost complex structures
- 1.3. Hermitian and K¨ahler metrics
- 1.4. Covariant derivatives and curvature
- 1.5. Vector bundles
- 1.6. Connections and curvature of line bundles
- 1.7. Line bundles and projective embeddings
- Chapter 2. Analytic Preliminaries
- 2.1. Harmonic functions on Rn
- 2.2. Elliptic differential operators
- 2.3. Schauder estimates
- 2.4. The Laplace operator on K¨ahler manifolds
- Chapter 3. K¨ahler-Einstein Metrics
- 3.1. The strategy
- 3.2. The C0- and C2-estimates
- 3.3. The C3- and higher-order estimates
- 3.4. The case c1(M) = 0
- 3.5. The case c1(M) >0
- 3.6. Futher reading
- Chapter 4. Extremal Metrics
- 4.1. The Calabi functional
- 4.2. Holomorphic vector fields and the Futaki invariant
- 4.3. The Mabuchi functional and geodesics
- 4.4. Extremal metrics on a ruled surface
- 4.5. Toric manifolds
- Chapter 5. Moment Maps and Geometric Invariant Theory
- 5.1. Moment maps
- 5.2. Geometric invariant theory (GIT)
- 5.3. The Hilbert-Mumford criterion
- 5.4. The Kempf-Ness theorem
- 5.5. Relative stability
- Chapter 6. K-stability
- 6.1. The scalar curvature as a moment map
- 6.2. The Hilbert polynomial and flat limits
- 6.3. Test-configurations and K-stability
- 6.4. Automorphisms and relative K-stability
- 6.5. Relative K-stability of a ruled surface
- 6.6. Filtrations
- 6.7. Toric varieties
- Chapter 7. The Bergman Kernel
- 7.1. The Bergman kernel
- 7.2. Proof of the asymptotic expansion
- 7.3. The equivariant Bergman kernel
- 7.4. The algebraic and geometric Futaki invariants
- 7.5. Lower bounds on the Calabi functional
- 7.6. The partial C0-estimate
- Chapter 8. CscK Metrics on Blow-ups
- 8.1. The basic strategy
- 8.2. Analysis in weighted spaces
- 8.3. Solving the non-linear equation when n > 2
- 8.4. The case when n = 2
- 8.5. The case when M admits holomorphic vector fields
- 8.6. K-stability of cscK manifolds
- Bibliography
- Index
