Holomorphic Morse Inequalities and Bergman Kernels
(Sprache: Englisch)
Winner of the Ferran Sunyer i Balaguer Prize 2006
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Produktinformationen zu „Holomorphic Morse Inequalities and Bergman Kernels “
Winner of the Ferran Sunyer i Balaguer Prize 2006
Klappentext zu „Holomorphic Morse Inequalities and Bergman Kernels “
This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
This book gives for the first time a self-contained and unified approach of holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel, and presents also various applications. The point of view comes from local index theory. The book opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are included, e.g., an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
Inhaltsverzeichnis zu „Holomorphic Morse Inequalities and Bergman Kernels “
0. Introduction1. Demailly's Holomorphic Morse Inequalities
2. Characterization of Moishezon Manifolds
3. Holomorphic Morse Inequalities on Non-compact Manifolds
4. Asymptotic Expansion of the Bergman Kernel
5. Kodaira Map
6. Bergman Kernel on Non-compact Manifolds
7. Toeplitz Operators
8. Bergman Kernels on Symplectic Manifolds
- Appendix
A. Sobolev Spaces
B. Elements of Analytic and Hermitian Geometry
C. Spectral Analysis of Self-adjoint Operators
D. Heat Kernel and Finite Propagation Speed
E. Harmonic Oscillator
Bibliographische Angaben
- Autoren: Weiping Ma , George Marinescu
- 2007, 2007, 422 Seiten, Maße: 15,5 x 24,4 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3764380969
- ISBN-13: 9783764380960
- Erscheinungsdatum: 19.07.2007
Sprache:
Englisch
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