Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature

Gong, Si-en; Liu, Hongyi; Xu, Bin

doi:10.1090/proc/14835

Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature
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by Si-en Gong, Hongyi Liu and Bin Xu PDF

Proc. Amer. Math. Soc. 148 (2020), 2179-2191 Request permission

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 $K=\{z=(z_1,\ldots , z_n)|z_1=z_2=0\}\subset \mathbb {C}^{n}$. 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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