TY  - JOUR
AU  - Guan, Qi’an
AU  - Mi, Zhitong
AU  - Yuan, Zheng
PY  - 2026
TI  - Optimal L2 Extension for Holomorphic Vector Bundles with Singular Hermitian Metrics
JO  - Peking Mathematical Journal
SN  - 2096-6075
SP  - 105
EP  - 193
VL  - 9
IS  - 1
AB  - In the present paper, we study the properties of singular Nakano positivity of singular Hermitian metrics on holomorphic vector bundles, and establish an optimal L2 extension theorem for holomorphic vector bundles with singular Hermitian metrics on weakly pseudoconvex Kähler manifolds, which is a unified version of the optimal L2 extension theorems for holomorphic line bundles with singular Hermitian metrics of Guan–Zhou and Zhou–Zhu. As applications, we give a necessary condition for the holding of the equality in optimal L2 extension theorem, and present singular Hermitian holomorphic vector bundle versions of some L2 extension theorems with optimal estimate.
UR  - https://doi.org/10.1007/s42543-024-00085-9
DO  - 10.1007/s42543-024-00085-9