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arXiv · 2203.07723

Boundary points, minimal $L^2$ integrals and concavity property II: on weakly pseudoconvex K\"ahler manifolds

Qi'an Guan·Zhitong Mi·Zheng Yuan
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Abstract

In this article, we consider minimal $L^2$ integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal $L^2$ integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to the modules, a strong openness property of the modules and a twisted version, an effectiveness result of the strong openness property of the modules.

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Qi'an Guan, Zhitong Mi, Zheng Yuan. 2022-03-15. Boundary points, minimal $L^2$ integrals and concavity property II: on weakly pseudoconvex K\"ahler manifolds. https://arxiv.org/abs/2203.07723

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