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arXiv · 2011.02660

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

Kang-Hyurk Lee
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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 K\"ahler-Einstein metric. We will also prove that if a bounded pseudoconvex domain admits a potential function of the K\"ahler-Einstein metric whose differential has constant length, then there is an $1$-parameter family of automorphisms.

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Kang-Hyurk Lee. 2020-11-05. A method of potential scaling in the study of pseudoconvex domains with noncompact automorphism group. https://arxiv.org/abs/2011.02660

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