From Holomorphic Functions to Complex Manifolds
He also proved various important theorems, including Levi's Problem and the coherence of higher direct image sheaves. Professor Grauert is the author of 10 books and his Selected Papers was published by Springer in 1994
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2002, 2002
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| Edition: | 1st ed. 2002 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Holomorphic Functions
- 1. Complex Geometry
- 2. Power Series
- 3. Complex Differentiable Functions
- 4. The Cauchy Integral
- 5. The Hartogs Figure
- 6. The Cauchy-Riemann Equations
- 7. Holomorphic Maps
- 8. Analytic Sets
- II Domains of Holomorphy
- 1. The Continuity Theorem
- 2. Plurisubharmonic Functions
- 3. Pseudoconvexity
- 4. Levi Convex Boundaries
- 5. Holomorphic Convexity
- 7. Examples and Applications
- 8. Riemann Domains over Cn
- 9. The Envelope of Holomorphy
- III Analytic Sets
- 1. The Algebra of Power Series
- 2. The Preparation Theorem
- 3. Prime Factorization
- 4. Branched Coverings
- 5. Irreducible Components
- 6. Regular and Singular Points
- IV Complex Manifolds
- 1. The Complex Structure
- 2. Complex Fiber Bundles
- 3. Cohomology
- 4. Meromorphie Functions and Divisors
- 5. Quotients and Submanifolds
- 6. Branched Riemann Domains
- 7. Modifications and Toric Closures
- V Stein Theory
- 1. Stein Manifolds
- 2. The Levi Form
- 3. Pseudoconvexity
- 4. Cuboids
- 5. Special Coverings
- 6. The Levi Problem
- VI Kahler Manifolds
- 1. Differential Forms
- 2. Dolbeault Theory
- 3. Kähler Metrics
- 4. The Inner Product
- 5. Hodge Decomposition
- 6. Hodge Manifolds
- 7. Applications
- VII Boundary Behavior
- 1. Strongly Pseudoconvex Manifolds
- 2. Subelliptic Estimates
- 3. Nebenhüllen
- 4. Boundary Behavior of Biholomorphic Maps
- References
- Index of Notation