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

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Abstract

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.

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Authors and Affiliations

  1. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Qi’An Guan

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Qi’An Guan

  3. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    XiangYu Zhou

  4. Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, China

    XiangYu Zhou

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  1. Qi’An Guan
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  2. XiangYu Zhou
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Correspondence to XiangYu Zhou.

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Guan, Q., Zhou, X. Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa. Sci. China Math. 58, 35–59 (2015). https://doi.org/10.1007/s11425-014-4946-4

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