Optimal $L^2$ extension for holomorphic vector bundles with singular hermitian metrics
Complex Variables
2023-03-15 v4 Differential Geometry
Abstract
In the present paper, we study the properties of singular Nakano positivity of singular hermitian metrics on holomorphic vector bundles, and establish an optimal extension theorem for holomorphic vector bundles with singular hermitian metrics on weakly pseudoconvex K\"{a}hler manifolds. As applications, we give a necessary condition for the holding of the equality in optimal extension theorem, and present singular hermitian holomorphic vector bundle versions of some extension theorems with optimal estimate.
Keywords
Cite
@article{arxiv.2210.06026,
title = {Optimal $L^2$ extension for holomorphic vector bundles with singular hermitian metrics},
author = {Qi'an Guan and Zhitong Mi and Zheng Yuan},
journal= {arXiv preprint arXiv:2210.06026},
year = {2023}
}
Comments
76pages, comments are welcomed. Some typos are corrected