English

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 L2L^2 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 L2L^2 extension theorem, and present singular hermitian holomorphic vector bundle versions of some L2L^2 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