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Boundary Points, Minimal \(L^2\) Integrals and Concavity Property : Vector Bundles

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Abstract

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal \(L^2\) integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex Kähler manifolds related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal \(L^2\) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a strong openness property of the modules and a twisted version, an effectiveness result of the strong openness property of the modules, and an optimal support function related to the modules.

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Acknowledgements

The authors would like to thank Dr. Shijie Bao for checking the manuscript. The first author and the second author were supported by National Key R &D Program of China 2021YFA1003100. The first author was supported by NSFC-11825101, NSFC-11522101 and NSFC-11431013. The second author was supported by China Postdoctoral Science Foundation 2022T150687.

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  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

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  1. Qi’an Guan
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Guan, Q., Mi, Z. & Yuan, Z. Boundary Points, Minimal \(L^2\) Integrals and Concavity Property : Vector Bundles. J Geom Anal 33, 305 (2023). https://doi.org/10.1007/s12220-023-01371-1

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