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Concavity Property of Minimal \(L^2\) Integrals with Lebesgue Measurable Gain V–Fibrations Over Open Riemann Surfaces

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Abstract

In this article, we present characterizations of the concavity property of minimal \(L^2\) integrals degenerating to linearity in the case of fibrations over open Riemann surfaces. As applications, we obtain characterizations of the holding of equality in optimal jets \(L^2\) extension problem from fibers over analytic subsets to fibrations over open Riemann surfaces, which implies characterizations of the fibration versions of the equality parts of Suita conjecture and extended Suita conjecture.

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Acknowledgements

The authors would like to thank Dr. Zhitong Mi for checking this paper and pointing out some mistakes. The second named author was supported by National Key R &D Program of China 2021YFA1003100, NSFC-11825101, NSFC-11522101 and NSFC-11431013.

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

    Shijie Bao

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

    Qi’an Guan & Zheng Yuan

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  1. Shijie Bao
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Bao, S., Guan, Q. & Yuan, Z. Concavity Property of Minimal \(L^2\) Integrals with Lebesgue Measurable Gain V–Fibrations Over Open Riemann Surfaces. J Geom Anal 33, 179 (2023). https://doi.org/10.1007/s12220-023-01234-9

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