具有LEBESGUE可测增益的极小积分的凹性

Pub Date : 2023-06-05 DOI:10.1017/nmj.2023.12

Q. Guan, Zheng Yuan

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引用次数: 10

摘要

在本文中，我们给出了与具有Lebesgue可测量增益的乘法器理想槽轮有关的最小$L^{2}$积分的凹性。作为应用，我们给出了凹性退化为线性的必要条件，一维情况的特征，以及在具有权重的开Riemann曲面上最优$L^2$扩张问题中等式成立的特征可能不是次调和的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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CONCAVITY PROPERTY OF MINIMAL INTEGRALS WITH LEBESGUE MEASURABLE GAIN

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.

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