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A study of variations of pseudoconvex domains via Kähler-Einstein metrics

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This paper is a sequel to Choi (Math Ann 362(1–2):121–146, 2015) 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.

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Acknowledgments

First of all, the author would like to thank Professor Jun-Muk Hwang for suggesting this problem, sharing his ideas, and for his constant support. He would also like to thank Bo Berndtsson, Mihai Pǎun and Georg Schumacher for many helpful advices and discussions and thank Xu Wang for helpful comments about the local triviality. The author was supported by TJ Park Science Fellowship funded by POSCO TJ Park Foundation.

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  1. School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegiro Dongdaemun-gu, Seoul, 130-722, Republic of Korea

    Young-Jun Choi

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  1. Young-Jun Choi
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Correspondence to Young-Jun Choi.

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Choi, YJ. A study of variations of pseudoconvex domains via Kähler-Einstein metrics. Math. Z. 281, 299–314 (2015). https://doi.org/10.1007/s00209-015-1484-x

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  • DOI: https://doi.org/10.1007/s00209-015-1484-x

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