從全純函數到復流形（簡體書）

本書是一部介紹復流形理論的入門書籍。作者用盡可能簡單的方法使讀者熟悉多變量復分析中的重要分支和方法，所以避免出現比較抽象的概念，如，層、凝聚和高維上同調等，僅運用了基本方法冪級數、正則向量叢和一維上閉鏈。然而，解析集Remmert-Stein定理，正則向量叢中的截面空間有限定理以及Levi問題解這些深層次的都得到了完整的證明。每章的結束都有大量的例子和練習。具備實分析、代數、拓撲以及單變量理論知識就可以完全讀懂這本書。本書可以作為學習多變量的入門教程，也是一本很好的參考書。
讀者對象：本書適用于數學專業的廣大師生。

Preface
I　Holomorphic Functions
　1.Complex Geometry
Real and Complex Structures
Hermitian Forms and Inner Products
Balls and Polydisks
Connectedness
Reinhardt Domains
　2.Power Series
Polynomials
Convergence
Power Series
　3.Complex Differentiable Functions
The Complex Gradient
Weakly Holomorphic Functions
Holomorphic Functions
　4.The Cauchy Integral
The Integral Formula
Holomorphy of the Derivatives
The Identity Theorem
　5.The Hartogs Figure
Expansion in Reinhardt Domains
Hartogs Figures
　6.The Cauchy-Riemann Equations
Real Differentiable Functions
Wirtingers Calculus
The Cauchy-Riemann Equations
　7.Holomorphic Maps
The Jacobian
Chain Rules
Tangent Vectors
The Inverse Mapping
　8.Analytic Sets
Analytic Subsets
Bounded Holomorphic Functions
Regular Points
Injective Holomorphic Mappings
II Domains of Holomorphy
　1.The Continuity Theorem
General Hartogs Figures
Removable Singularities
The Continuity Principle
Hartogs Convexity
Domains of Holomorphy
　2.Plurisubharmonic Functions
Subharmonic Functions
The Maximum Principle
Differentiable Subharmonic Functions
Plurisubharmonic Functions
The Levi Form
Exhaustion Functions
　3.Pseudoconvexity
Pseudoconvexity
The Boundary Distance
Properties of Pseudoconvex Domains
　4.Levi Convex Boundaries
Boundary Functions
The Levi Condition
Affine Convexity
A Theorem of Levi
　5.Holomorphic Convexity
Affine Convexity
Holomorphic Convexity
The Cartan-Thullen Theorem
　6.Singular Functions
Normal Exhaustions
Unbounded Holomorphic Functions
Sequences
　7.Examples and Applications
Domains of Holomorphy
Complete Reinhardt Domains
Analytic Polyhedra
　8.Riemann Domains over Cn
Riemann Domains
Union of Riemann Domains
　9.The Envelope of Holomorphy
Holomorphy on Riemann Domains
Envelopes of Holomorphy
Pseudoconvexity
Boundary Points
Analytic Disks
III　Analytic Sets
IV　Complex Mannifolds
V Stein Theory
VI Kahler Manifolds
VII Boundary Behavior
References
Index of Notation
Index