Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 2021-2038.doi: 10.1007/s10473-021-0614-2

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L2 EXTENSIONS WITH SINGULAR METRICS ON KÄHLER MANIFOLDS

Xiangyu ZHOU1, Langfeng ZHU2   

  1. 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).

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

CLC Number: 

  • 32D15
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