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Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature


Authors: Si-en Gong, Hongyi Liu and Bin Xu
Journal: Proc. Amer. Math. Soc. 148 (2020), 2179-2191
MSC (2010): Primary 53B35, 32A10
DOI: https://doi.org/10.1090/proc/14835
Published electronically: January 28, 2020
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Abstract: Let $ n\ge 2$ be an integer, and let $ B^{n}\subset \mathbb{C}^{n}$ be the unit ball. Let $ K\subset B^{n}$ be a compact subset such that $ B^n\setminus K$ is connected, or $ K=\{z=(z_1,\ldots , z_n)\vert z_1=z_2=0\}\subset \mathbb{C}^{n}$. By the theory of developing maps, we prove that a Kähler metric on $ B^{n}\setminus K$ with constant holomorphic sectional curvature uniquely extends to $ B^{n}$.


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Si-en Gong
Affiliation: Wu Wen-Tsun Key Laboratory of Math, USTC, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China
Address at time of publication: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: gse@mail.ustc.edu.cn

Hongyi Liu
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
Email: hongyi@berkeley.edu

Bin Xu
Affiliation: Wu Wen-Tsun Key Laboratory of Math, USTC, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China
Email: bxu@ustc.edu.cn

DOI: https://doi.org/10.1090/proc/14835
Received by editor(s): January 2, 2019
Received by editor(s) in revised form: June 8, 2019, July 28, 2019, and September 3, 2019
Published electronically: January 28, 2020
Additional Notes: The third author was supported in part by the National Natural Science Foundation of China (Grant nos. 11571330 and 11971450) and the Fundamental Research Funds for the Central Universities.
Part of the work was completed while the third author was visiting the Institute of Mathematical Sciences at ShanghaiTech University in Spring 2019.
The third author is the corresponding author
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2020 American Mathematical Society