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Mathematics > Complex Variables

arXiv:2206.00443 (math)
[Submitted on 1 Jun 2022 (v1), last revised 19 Jun 2022 (this version, v2)]

Title:Boundary points, minimal $L^2$ integrals and concavity property V -- vector bundles

Authors:Qi'an Guan, Zhitong Mi, Zheng Yuan
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Abstract:In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal $L^2$ 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 $L^2$ 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.
Comments: 74 pages, some typos are corrected, and Lemma 9.3 was added. arXiv admin note: substantial text overlap with arXiv:2203.07723, arXiv:2203.15188
Subjects: Complex Variables (math.CV)
Cite as: arXiv:2206.00443 [math.CV]
  (or arXiv:2206.00443v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.2206.00443

Submission history

From: Qi'an Guan [view email]
[v1] Wed, 1 Jun 2022 12:24:24 UTC (48 KB)
[v2] Sun, 19 Jun 2022 13:37:28 UTC (48 KB)
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