On the uniqueness of conical Kähler-Einstein metrics

Abstract

The purpose of this paper is to prove the uniqueness of conical Kähler-Einstein metrics, under the condition that the twisted $Ding$-functional is proper. This is a generalization of the author's previous work, and we shall first investigate the uniqueness of twisted Kähler-Einstein metrics, and then use these smooth perturbed solutions to approximate the actual conical one. Finally, it will bring the uniqueness of the limiting singular metric.

References in corpus (4)

• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• A variational approach to complex Monge-Ampere equations
• A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics
• Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains