TY  - BOOK
AU  - Fritzsche, Klaus
AU  - Grauert, Hans
TI  - From holomorphic functions to complex manifolds
SN  - 9780387953953
U1  - 515.98 
PY  - 2002///
CY  - New York
PB  - Springer
KW  - Complex manifolds
KW  - Holomorphic functions
KW  - Mathematics
N1  - 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 --
6. Singular Functions --
7. Examples and Applications --
8. Riemann Domains over C[superscript n] --
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. Meromorphic Functions and Divisors --
5. Quotients and Submanifolds --
6. Branched Riemann Domain --
7. Modification 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 Algebra --
2. Dolbeault Theory --
3. Kahler Metrics --
4. The Inner Product --
5. Hodge Decomposition --
6. Hodge Manifolds --
7. Applications --
VII. Boundary Behavior --
1. Strongly Pseudoconvex Manifolds --
2. Subelliptic Estimates --
3. Nebenhullen --
4. Boundary Behavior of Biholomorphic Maps
ER  -