Complex monge-ampère equations and geodesics in the space of kähler metrics /

Complex monge-ampère equations and geodesics in the space of kähler metrics /

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Bibliographic Details
Imprint:	Berlin ; New York : Springer, ©2012.
Description:	1 online resource (viii, 310 pages).
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 2038 Lecture notes in mathematics (Springer-Verlag) ; 2038.
Subject:	Monge-Ampère equations. Geodesics (Mathematics) Kählerian structures. Geodesics (Mathematics) Kählerian structures. Monge-Ampère equations.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11076448

Hidden Bibliographic Details
Other authors / contributors:	Guedj, Vincent.
ISBN:	9783642236693 3642236693 3642236685 9783642236686 9783642236686
Notes:	Includes bibliographical references.
Summary:	Annotation The purpose of these lecture notes is to provide an introduction to the theory of complex MongeAmpère 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 (KählerEinstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after BedfordTaylor), MongeAmpère 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 Kähler 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.
Other form:	Printed edition: 9783642236686
Standard no.:	10.1007/978-3-642-23669-3

Table of 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-Ampère Equation
4. Probabilistic Approach to Regularity
III. Monge-Ampère Equations on Compact Manifolds
5. The Calabi-Yau Theorem
IV Geodesics in the Space of Kähler Metrics
6. The Riemannian Space of Kähler Metrics
7. MA Equations on Manifolds with Boundary
8. Bergman Geodesics.