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CONCAVITY PROPERTY OF MINIMAL $L^{2}$ INTEGRALS WITH LEBESGUE MEASURABLE GAIN

Part of: Holomorphic convexity Holomorphic fiber spaces Analytic continuation Genetics and population dynamics Pluripotential theory Differential operators in several variables

Published online by Cambridge University Press:  05 June 2023

QI’AN GUAN Open the ORCID record for QI’AN GUAN [Opens in a new window]  and
ZHENG YUAN Open the ORCID record for ZHENG YUAN [Opens in a new window]
QI’AN GUAN
Affiliation:
School of Mathematical Sciences Peking University Beijing 100871, China guanqian@math.pku.edu.cn
ZHENG YUAN*
Affiliation:
School of Mathematical Sciences Peking University Beijing 100871, China
*
zyuan@pku.edu.cn
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Abstract

In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity, characterizations for 1-dimensional case, and a characterization for the holding of the equality in optimal $L^2$ extension problem on open Riemann surfaces with weights may not be subharmonic.

MSC classification

Primary: 32D15: Continuation of analytic objects
Secondary: 32E10: Stein spaces, Stein manifolds 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results 32U05: Plurisubharmonic functions and generalizations 32W05: $overlinepartial$ and $overlinepartial$-Neumann operators

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Article
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Nagoya Mathematical Journal , Volume 252 , December 2023 , pp. 842 - 905
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

Qi’an Guan was supported by the National Key R&D Program of China (Grant No. 2021YFA1003100) and the National Natural Science Foundation of China (Grant No. NSFC-11825101, NSFC-11522101, and NSFC-11431013).

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