The Complex Monge-Ampere Equation and Pluripotential Theory

Slawomir Kolodziej - Collection Memoirs of the American Mathematical Society

64 pages, parution le 29/06/2006

Ajouter à une liste

Indisponible

Résumé

We collect here results on the existence and stability of weak solutions of complex Monge-Ampére equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampére equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampére equation on compact Kähler manifolds. This is a generalization of the Calabi-Yau theorem.

Sommaire

Positive currents and plurisubharmonic functions
Siciak's extremal function and a related capacity
The Dirichlet problem for the Monge-Ampère equation with continuous data
The Dirichlet problem continued
The Monge-Ampère equation for unbounded functions
The complex Monge-Ampère equation on a compact Kähler manifold
Bibliography

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Slawomir Kolodziej
Collection	Memoirs of the American Mathematical Society
Parution	29/06/2006
Nb. de pages	64
Format	17,5 x 25
Couverture	Broché
Poids	162g
Intérieur	Noir et Blanc
EAN13	9780821837634
ISBN13	978-0-8218-3763-4