Kaehler-Einstein fillings

Kaehler-Einstein fillings

We show that on an open bounded smooth strongly pseudoconvex subset of Cn, there exists a Kaehler-Einstein metric with positive Einstein constant, such that the metric restricted to the Levi distribution of the boundary is conformal to the Levi form. To achieve this, we solve an associated complex M...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the London Mathematical Society 2013-12, Vol.88 (3), p.737-760
Hauptverfasser: Guedj, Vincent, Kolev, Boris, Yeganefar, Nader
Format: Artikel
Sprache:eng
Schlagworte:
Boundaries
Boundary conditions
Constants
Constrictions
Dirichlet problem
Mathematical analysis
Monge-Ampere equation
Uniqueness
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We show that on an open bounded smooth strongly pseudoconvex subset of Cn, there exists a Kaehler-Einstein metric with positive Einstein constant, such that the metric restricted to the Levi distribution of the boundary is conformal to the Levi form. To achieve this, we solve an associated complex Monge-Ampere equation with Dirichlet boundary condition. We also prove uniqueness of the solution subject to additional restrictions.
ISSN:0024-6107
DOI:10.1112/jlms/jdt031