L2 EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS

doi:10.1007/s10473-021-0614-2

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 2021-2038.doi: 10.1007/s10473-021-0614-2

L² EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS

周向宇¹, 朱朗峰²

1. Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2021-04-01 修回日期:2021-08-24 出版日期:2021-12-25 发布日期:2021-12-27
通讯作者: Xiangyu ZHOU,E-mail:xyzhou@math.ac.cn E-mail:xyzhou@math.ac.cn
作者简介:Langfeng ZHU,E-mail:zhulangfeng@amss.ac.cn
基金资助:
Xiangyu Zhou was partially supported by the National Natural Science Foundation of China (11688101 and 11431013). Langfeng Zhu was partially supported by the National Natural Science Foundation of China (12022110, 11201347 and 11671306).

L² EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS

Xiangyu ZHOU¹, Langfeng ZHU²

1. Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2021-04-01 Revised:2021-08-24 Online:2021-12-25 Published:2021-12-27
Supported by:
Xiangyu Zhou was partially supported by the National Natural Science Foundation of China (11688101 and 11431013). Langfeng Zhu was partially supported by the National Natural Science Foundation of China (12022110, 11201347 and 11671306).

摘要/Abstract

摘要： In this paper, we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of (pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics, and also discuss their applications and the ideas contained in the proofs.

关键词: singular metric, optimal L² extension theorem, strong openness of multiplier ideal sheaf, generalized Siu's lemma, weakly pseudoconvex Kähler manifold

Abstract: In this paper, we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of (pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics, and also discuss their applications and the ideas contained in the proofs.

Key words: singular metric, optimal L² extension theorem, strong openness of multiplier ideal sheaf, generalized Siu's lemma, weakly pseudoconvex Kähler manifold

中图分类号:

32D15

周向宇, 朱朗峰. L² EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS[J]. 数学物理学报(英文版), 2021, 41(6): 2021-2038.

Xiangyu ZHOU, Langfeng ZHU. L² EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS[J]. Acta mathematica scientia,Series B, 2021, 41(6): 2021-2038.

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L² EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS

L² EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS

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