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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor Corporativo: SpringerLink (Online service)
Otros Autores: Guedj, Vincent (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
Edición:1st ed. 2012.
Colección:Lecture Notes in Mathematics, 2038
Temas:
Functions of complex variables.
Geometry, Differential.
Differential equations.
Algebraic geometry.
Several Complex Variables and Analytic Spaces.
Differential Geometry.
Differential Equations.
Algebraic Geometry.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

Ejemplares similares