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Original Article

Concavity of Minimal L2 Integrals Related to Multiplier Ideal Sheaves

School of Mathematical Sciences, Peking University, Beijing 100871, China
Present Address: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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Abstract

In this article, we present the concavity of the minimal L2 integrals related to multiplier ideals sheaves on Stein manifolds. As applications, we obtain a necessary condition for the concavity degenerating to linearity, a characterization for 1-dimensional case, and a characterization for the equality in 1-dimensional optimal L2 extension problem to hold.

Keywords

Strong openness conjectureMultiplier ideal sheafPlurisubharmonic functionSublevel set

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Peking Mathematical Journal
Volume 6 Issue 2,
September 2023
Pages 393-457
DOI: 10.1007/s42543-021-00047-5

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Cite this article:
Guan, Q., Mi, Z. Concavity of Minimal L2 Integrals Related to Multiplier Ideal Sheaves. Peking Math J 6, 393-457 (2023). https://doi.org/10.1007/s42543-021-00047-5

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Received: 01 June 2021
Revised: 26 September 2021
Accepted: 04 October 2021
Published: 22 January 2022
© Peking University 2022