Subharmonicity of the variations of Kähler-Einstein metrics on pseudoconvex domains

Abstract

This paper is a sequel to \cite{Choi} in Math. Ann. In that paper we studied the subharmonicity of Kähler-Einstein metrics on strongly pseudoconvex domains of dimension greater than or equal to $3$. In this paper, we study the variations Kähler-Einstein metrics on bounded strongly pseudoconvex domains of dimension $2$. In addition, we discuss the previous result with general bounded pseudoconvex domain and local triviality of a family of bounded strongly pseudoconvex domains.

15 pages

References in corpus (2)

• Positivity of relative canonical bundles for families of canonically polarized manifolds
• Dynamical construction of Kähler-Einstein metrics on bounded pseudoconvex domains