Science China Mathematics

, Volume 60, Issue 6, pp 967–976 | Cite as

Strong openness of multiplier ideal sheaves and optimal L 2 extension

  • Qi’An GuanEmail author
  • XiangYu Zhou


In this paper, we reveal that our solution of Demailly’s strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Kollár and Jonsson-Mustată implies the truth of twisted versions of the strong openness conjecture; our optimal L 2 extension implies Berndtsson’s positivity of vector bundles associated to holomorphic fibrations over a unit disc.


strong openness conjecture plurisubharmonic function multiplier ideal sheaf optimal L2 extension theorem 


32D15 32E10 32L10 32W05 32U05 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina
  2. 2.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina
  3. 3.Institute of Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  4. 4.Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijingChina

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