Boundary points, minimal L² integrals and concavity property II: on\n weakly pseudoconvex K "ahler manifolds

2022/03/15 by Qi’an Guan, Guan, Qi'an, Zhitong Mi +3
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2203.07723

Abstract

In this article, we consider minimal L² integrals on the sublevel sets of\nplurisubharmonic functions on weakly pseudoconvex K "ahler manifolds with\nLebesgue measurable gain related to modules at boundary points of the sublevel\nsets, and establish a concavity property of the minimal L² integrals. As\napplications, we present a necessary condition for the concavity degenerating\nto linearity, a concavity property related to modules at inner points of the\nsublevel sets, an optimal support function related to the modules, a strong\nopenness property of the modules and a twisted version, an effectiveness result\nof the strong openness property of the modules.\n

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