Boundary points, minimal L² integrals and concavity property V -- vector bundles

2022/06/01 by Qi’an Guan, Guan, Qi'an, Zhitong Mi +3
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2206.00443

openalex publication_date 2022/06/01 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal L² integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex Kähler manifolds related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L² integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a strong openness property of the modules and a twisted version, an effectiveness result of the strong openness property of the modules, and an optimal support function related to the modules.

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