Concavity property of minimal $L^{2}$ integrals with Lebesgue measurable gain VIII -- partial linearity and log-convexity

Shijie Bao; Qi'an Guan; Zheng Yuan

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arXiv · 2307.07112

Concavity property of minimal $L^{2}$ integrals with Lebesgue measurable gain VIII -- partial linearity and log-convexity

Shijie Bao·Qi'an Guan·Zheng Yuan

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Abstract

In this article, we give some necessary conditions for the concavity property of minimal $L^2$ integrals degenerating to partial linearity, a charaterization for the concavity degenerating to partial linearity for open Riemann surfaces, and some relations between the concavity property for minimal $L^2$ integrals and the log-convexity for Bergman kernels.

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Shijie Bao, Qi'an Guan, Zheng Yuan. 2023-07-14. Concavity property of minimal $L^{2}$ integrals with Lebesgue measurable gain VIII -- partial linearity and log-convexity. https://arxiv.org/abs/2307.07112

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