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Boundary points, minimal L2 integrals and concavity property II: Weakly pseudoconvex Kähler manifolds

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Abstract

In this paper, we consider minimal L2 integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex Kähler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L2 integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

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Acknowledgements

The first author and the second author were supported by National Key R&D Program of China (Grant No. 2021YFA1003100). The first author was supported by National Natural Science Foundation of China (Grant Nos. 11825101, 11522101 and 11431013). The second author was supported by the Talent Fund of Beijing Jiaotong University. The third author was supported by China Postdoctoral Science Foundation (Grant Nos. BX20230402 and 2023M743719).

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Authors and Affiliations

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

    Qi’an Guan & Zheng Yuan

  2. School of Mathematics and Statistics, Beijing Jiaotong University, Beijing, 100044, China

    Zhitong Mi

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

    Zhitong Mi & Zheng Yuan

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  1. Qi’an Guan
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  2. Zhitong Mi
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  3. Zheng Yuan
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Correspondence to Qi’an Guan.

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Guan, Q., Mi, Z. & Yuan, Z. Boundary points, minimal L2 integrals and concavity property II: Weakly pseudoconvex Kähler manifolds. Sci. China Math. (2024). https://doi.org/10.1007/s11425-022-2257-3

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