English

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

Complex Variables 2022-06-22 v2

Abstract

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal L2L^2 integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L2L^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.

Keywords

Cite

@article{arxiv.2206.00443,
  title  = {Boundary points, minimal $L^2$ integrals and concavity property V -- vector bundles},
  author = {Qi'an Guan and Zhitong Mi and Zheng Yuan},
  journal= {arXiv preprint arXiv:2206.00443},
  year   = {2022}
}

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

R2 v1 2026-06-24T11:35:53.129Z