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Title Complex monge-ampere equations and geodesics in the space of kahler metrics / Vincent Guedj, editor.
Imprint Berlin ; New York : Springer, 2012.

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Series Lecture notes in mathematics, 0075-8434 ; 2038
Lecture notes in mathematics (Springer-Verlag) ; 2038.
Subject Monge-Ampère equations.
Geodesics (Mathematics)
Kählerian structures.
Alt Name Guedj, Vincent.
Description 1 online resource (viii, 310 pages).
polychrome rdacc
Bibliography Note Includes bibliographical references.
Summary Annotation The purpose of these lecture notes is to provide an introduction to the theory of complex MongeAmpere operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kahler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (KahlerEinstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after BedfordTaylor), MongeAmpere 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 CalabiYau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kahler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of CaffarelliKohnNirenbergSpruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after PhongSturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures byR. 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.
Contents 1. Introduction -- I. The Local Homogenious Dirichlet Problem.-2. Dirichlet Problem in Domains of Cn -- 3. Geometric Maximality -- II. Stochastic Analysis for the Monge-Ampere Equation -- 4. Probabilistic Approach to Regularity -- III. Monge-Ampere Equations on Compact Manifolds -- 5. The Calabi-Yau Theorem -- IV Geodesics in the Space of Kahler Metrics -- 6. The Riemannian Space of Kahler Metrics -- 7. MA Equations on Manifolds with Boundary -- 8. Bergman Geodesics.
ISBN 9783642236693 (electronic bk.)
3642236693 (electronic bk.)
3642236685 (print)
9783642236686 (print)
ISBN/ISSN 10.1007/978-3-642-23669-3
OCLC # 773291552
Additional Format Printed edition: 9783642236686

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