Skip to main content
SpringerLink
Log in

Characterizations of plurisubharmonic functions

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

We give characterizations of (quasi-)plurisubharmonic functions in terms of Lp-estimates of \(\overline{\partial}\) and Lp-extensions of holomorphic functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berndtsson B. L2-methods for the ∂-equation. http://www.math.chalmers.se/∼bob/not3.pdf, 1995

  2. Berndtsson B. Prekopa’s theorem and Kiselman’s minimum principle for plurisubharmonic functions. Math Ann, 1998, 312: 785–792

    Article  MathSciNet  Google Scholar 

  3. Berndtsson B. Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains. Ann Inst Fourier Grenoble, 2006, 56: 1633–1662

    Article  MathSciNet  Google Scholar 

  4. Berndtsson B. Curvature of vector bundles associated to holomorphic fibrations. Ann of Math (2), 2009, 169: 531–560

    Article  MathSciNet  Google Scholar 

  5. Błocki Z. Suita conjecture and the Ohsawa-Takegoshi extension theorem. Invent Math, 2013, 193: 149–158

    Article  MathSciNet  Google Scholar 

  6. Demailly J-P. Regularization of closed positive currents and intersection theory. J Algebraic Geom, 1992, 1: 361–409

    MathSciNet  MATH  Google Scholar 

  7. Demailly J-P. Analytic Methods in Algebraic Geometry. Surveys of Modern Mathematics, vol. 1. Somerville: International Press; Beijing: Higher Education Press, 2012

    MATH  Google Scholar 

  8. Deng F S, Ning J F, Wang Z W, Zhou X Y. Positivity of holomorphic vector bundles in terms of Lp-properties of \(\overline{\partial}\). arXiv:2001.01762, 2020

  9. Deng F S, Wang Z W, Zhang L Y, Zhou X Y. New characterization of plurisubharmonic functions and positivity of direct image sheaves. arXiv:1809.10371, 2018

  10. Guan Q A, Zhou X Y. Optimal constant problem in the L2 extension theorem. C R Math Acad Sci Paris, 2012, 350: 753–756

    Article  MathSciNet  Google Scholar 

  11. Guan Q A, Zhou X Y. A solution of an L2 extension problem with an optimal estimate and applications. Ann of Math (2), 2015, 181: 1139–1208

    Article  MathSciNet  Google Scholar 

  12. Hacon C, Popa M, Schnell C. Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun. In: Local and Global Methods in Algebraic Geometry. Contemporary Mathematics, vol. 712. Providence: Amer Math Soc, 2018, 143–195

    Chapter  Google Scholar 

  13. Hörmander L. L2 estimates and existence theorems for the \(\overline{\partial}\) operator. Acta Math, 1965, 113: 89–152

    Article  MathSciNet  Google Scholar 

  14. Hosono G, Inayama T. A converse of Hörmander’s L2-estimate and new positivity notions for vector bundles. arXiv:1901.02223v1, 2019

  15. Ohsawa T, Takegoshi K. On the extension of L2 holomorphic functions. Math Z, 1987, 195: 197–204

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11871451, 12071485 and 12071035). The first author was supported by the University of Chinese Academy of Sciences. The third author was supported by Beijing Natural Science Foundation (Grant Nos. 1202012 and Z190003). The authors are very grateful to Professor Xiangyu Zhou, their former advisor, for helpful discussions on related topics. The authors thank the anonymous referees for careful reading of the manuscript and helpful suggestions.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Fusheng Deng

  2. School of Mathematics and Statistics HNP-LAMA, Central South University, Changsha, 410083, China

    Jiafu Ning

  3. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Zhiwei Wang

Authors
  1. Fusheng Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiafu Ning
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiwei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiafu Ning.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, F., Ning, J. & Wang, Z. Characterizations of plurisubharmonic functions. Sci. China Math. 64, 1959–1970 (2021). https://doi.org/10.1007/s11425-021-1873-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-021-1873-y

Keywords

MSC(2020)

Search

Navigation