A method of potential scaling in the study of pseudoconvex domains with noncompact automorphism group

Abstract

The affine scaling method has been a typical approach to study complex domains with noncompact automorphism group. In this article, we will introduce an alternative approach, so called, the method of potential scaling to construct a certain class of potential functions of the Kahler-Einstein metric. We will also prove that if a bounded pseudoconvex domain admits a potential function of the Kahler-Einstein metric whose differential has constant length, then there is an 1-parameter family of automorphisms. (C) 2021 Elsevier Inc. All rights reserved.