Science China Mathematics

, Volume 58, Issue 1, pp 35–59 | Cite as

Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa

  • Qi’An Guan
  • XiangYu ZhouEmail author
Articles Progress of Projects Supported by NSFC


In this paper, we solve the optimal constant problem in the setting of Ohsawa’s generalized L 2 extension theorem. As applications, we prove a conjecture of Ohsawa and the extended Suita conjecture, we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.


L2 extension theorem optimal L2 estimate Bergman kernel a conjecture of Ohsawa extended Suita conjecture 


Primary 32D15, 32E10, 32A25, 32L10, 32U05 Secondary 32W05, 14H55, 32Q28 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina
  2. 2.School of Mathematical SciencesPeking 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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