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

2020/11/05 by Lee, Kang-Hyurk
#32M05 #32M25 #32Q20 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.02660

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 Kähler-Einstein metric. We will also prove that if a bounded pseudoconvex domain admits a potential function of the Kähler-Einstein metric whose differential has constant length, then there is an 1-parameter family of automorphisms.

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