Geometry And Analysis on Manifolds

Editors: Adiprasito, Karim, Bárány, Imre, Vilcu, Costin (Eds.)
Includes overviews of evolving areas in convexity, discrete geometry and graph theory
Presents easily understandable, but surprising, properties, obtained using topological, geometric and graph theoretic tools
Written by experts from all over the word

Editors: Alpay, D., Cipriani, F., Colombo, F., Guido, D., Sabadini, I., Sauvageot, J.-L. (Eds.)
Covers several aspects of the current research activity in operator theory, operator algebras and applications, which are rarely brought together in the same volume
Presents an updated state-of-the-art of the current research of several first rate mathematicians

In 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.

In 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.