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From holomorphic functions to complex manifolds/ Klaus Fritzsche and Hans Grauert

By: Fritzsche, KlausContributor(s): Grauert, HansMaterial type: Text

TextSeries: (Graduate texts in mathematics) ; 213Publication details: New York: Springer, 2002Description: xv, 392 p. : ill. ; 24 cmISBN: 9780387953953Subject(s): Complex manifolds | Holomorphic functions | MathematicsDDC classification: 515.98

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 -- 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.

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Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	515.98 FRI/ (Browse shelf(Opens below))	Available		P25220

Total holds: 0

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Previous	515.93 JOH/F Functions of one complex variable II //	515.94 FAR/A Analysis and geometry on complex homogeneous domains/	515.94 GRA/S Several complex variables/	515.98 FRI/ From holomorphic functions to complex manifolds/	515.98 MUJ/C Complex analysis in Banach spaces/	515.98 RAN/H Holomorphic Functions and Integral Representations in Several Complex Variables/	515.983 SER / Elliptic functions/	Next

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.

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