Differential Analysis on Complex ManifoldsIn developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of the developments in the field during the decades since the book appeared. From a review of the 2nd Edition: - Nigel Hitchin, Bulletin of the London Mathematical Society
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Contents
Manifolds and Vector Bundles | 1 |
Sheaf Theory | 36 |
Differential Geometry | 65 |
Elliptic Operator Theory | 108 |
Compact Complex Manifolds | 154 |
Kodairas Projective Embedding Theorem | 217 |
Appendix by Oscar GarcíaPrada | 241 |
Higgs Bundles on Riemann Surfaces | 253 |
Nonabelian Hodge Theory | 261 |
| 284 | |