9783642236686 - Complex Monge?Ampère Equations and Geodesics in the Space of Kähler Metrics (Lecture Notes in Mathematics, Band 2038) (4 Ergebnisse)

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Paperback. Zustand: Brand New. 2012 edition. 318 pages. 9.00x6.00x0.75 inches. In Stock.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The purpose of these lecture notes is to provide an introduction to the theory of complex Monge-Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary).These operators are of central use in several fundamental problems of complex differential geometry (Kähler-Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford-Taylor), Monge-Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi-Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli-Kohn-Nirenberg-Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong-Sturm and Berndtsson).Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Taschenbuch. Zustand: Neu. Complex Monge-Ampère Equations and Geodesics in the Space of Kähler Metrics | Vincent Guedj | Taschenbuch | Lecture Notes in Mathematics | viii | Englisch | 2012 | Springer | EAN 9783642236686 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.