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

• Corporate Author: SpringerLink (Online service)
• Other Authors: Guedj, Vincent (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Series: Lecture Notes in Mathematics, 2038
• Subjects: Mathematics.; Algebraic geometry.; Partial differential equations.; Functions of complex variables.; Differential geometry.; Several Complex Variables and Analytic Spaces.; Differential Geometry.; Partial Differential Equations.; Algebraic Geometry.

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 fun...

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.