Complex Monge-Ampère Equations and Geodesics in the Space of Kähler Metrics

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 f...

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Bibliographic Details
Call Number:Libro Electrónico
Corporate Author: SpringerLink (Online service)
Other Authors: Guedj, Vincent (Editor)
Format: Electronic eBook
Language:Inglés
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
Edition:1st ed. 2012.
Series:Lecture Notes in Mathematics, 2038
Subjects:
Functions of complex variables.
Geometry, Differential.
Differential equations.
Algebraic geometry.
Several Complex Variables and Analytic Spaces.
Differential Geometry.
Differential Equations.
Algebraic Geometry.
Online Access:Texto Completo
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.

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