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arXiv · 2209.03637

Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain

Qi'an Guan·Zheng Yuan
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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.

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Qi'an Guan, Zheng Yuan. 2022-09-08. Concavity property of minimal $L^2$ integrals with Lebesgue measurable gain. https://arxiv.org/abs/2209.03637

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