Mathematical Theory and Applications ›› 2021, Vol. 41 ›› Issue (3): 1-12.

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Extension of Quasi-plurisubharmonic Functions

  

  1. 1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, China; 2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China; 3. Institute of Mathematics, Academy of Mathematics and Systems Sciences and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China; 4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
  • Online:2021-09-30 Published:2021-10-28
  • Contact: Zhiwei Wang (1986-), Associate Professor, Research field: Sevaral Complex Variables and Complex Geometry; E-mail: zhiwei@bnu.edu.cn
  • Supported by:

    The first author is partially supported by the NSFC grant(12071485).

    The second author is partially supported by the Beijing Natural Science Foundation (1202012, Z190003) and the NSFC grant (11701031,12071035).

    The third author is partially supported by the NSFC grant (11688101).

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Abstract:

In this paper, we give a survey on the extension of (quasi-)plurisubharmonic functions from complex submanifolds.

We firstly review the extension of plurisubharmonic functions on Stein manifolds, and then review the extension of quasi-plurisubharmonic functions on compact complex manifolds, including some unpublished new results of the authors Wang and Zhou.

Key words: Stein manifold; , Plurisubharmonic function; , K?hler manifold; , Extension

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