Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature

Si En Gong; Hongyi Liu; Bin Xu

doi:10.1090/proc/14835

Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature

Si En Gong, Hongyi Liu, Bin Xu

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let n ≥ 2 be an integer, and let Bⁿ ⊂ Cⁿ be the unit ball. Let K ⊂ Bⁿ be a compact subset such that Bⁿ \ K is connected, or K = {z = (z1,..., z_n)|z1 = z2 = 0} ⊂ Cⁿ. By the theory of developing maps, we prove that a Kähler metric on Bⁿ \K with constant holomorphic sectional curvature uniquely extends to Bⁿ.

Original language	English (US)
Pages (from-to)	2179-2191
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	5
DOIs	https://doi.org/10.1090/proc/14835
State	Published - 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/proc/14835

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title = "Locally removable singularities for K{\"a}hler metrics with constant holomorphic sectional curvature",

abstract = "Let n ≥ 2 be an integer, and let Bn ⊂ Cn be the unit ball. Let K ⊂ Bn be a compact subset such that Bn \textbackslash{} K is connected, or K = \{z = (z1,..., zn)|z1 = z2 = 0\} ⊂ Cn. By the theory of developing maps, we prove that a K{\"a}hler metric on Bn \textbackslash{}K with constant holomorphic sectional curvature uniquely extends to Bn.",

author = "Gong, \{Si En\} and Hongyi Liu and Bin Xu",

note = "Publisher Copyright: {\textcopyright} 2020 American Mathematical Society.",

year = "2020",

doi = "10.1090/proc/14835",

language = "English (US)",

volume = "148",

pages = "2179--2191",

journal = "Proceedings of the American Mathematical Society",

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T1 - Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature

AU - Gong, Si En

AU - Liu, Hongyi

AU - Xu, Bin

PY - 2020

Y1 - 2020

N2 - Let n ≥ 2 be an integer, and let Bn ⊂ Cn be the unit ball. Let K ⊂ Bn be a compact subset such that Bn \ K is connected, or K = {z = (z1,..., zn)|z1 = z2 = 0} ⊂ Cn. By the theory of developing maps, we prove that a Kähler metric on Bn \K with constant holomorphic sectional curvature uniquely extends to Bn.

AB - Let n ≥ 2 be an integer, and let Bn ⊂ Cn be the unit ball. Let K ⊂ Bn be a compact subset such that Bn \ K is connected, or K = {z = (z1,..., zn)|z1 = z2 = 0} ⊂ Cn. By the theory of developing maps, we prove that a Kähler metric on Bn \K with constant holomorphic sectional curvature uniquely extends to Bn.

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DO - 10.1090/proc/14835

M3 - Article

AN - SCOPUS:85082920702

SN - 0002-9939

VL - 148

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

Locally removable singularities for Kähler metrics with constant holomorphic sectional curvature

Abstract

All Science Journal Classification (ASJC) codes

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