Boundary points, minimal $L^2$ integrals and concavity property II: on weakly pseudoconvex Kähler manifolds
Abstract
In this article, we consider minimal $L^2$ integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex Kähler 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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.07723
- arXiv:
- arXiv:2203.07723
- Bibcode:
- 2022arXiv220307723G
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Algebraic Geometry
- E-Print:
- 65 pages, some typos are corrected