Boundary points, minimal $L^2$ integrals and concavity property V -- vector bundles
Abstract
In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal 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 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.
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