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arXiv · 2210.06026

Optimal $L^2$ extension for holomorphic vector bundles with singular hermitian metrics

Qi'an Guan·Zhitong Mi·Zheng Yuan
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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 $L^2$ 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 $L^2$ extension theorem, and present singular hermitian holomorphic vector bundle versions of some $L^2$ extension theorems with optimal estimate.

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Qi'an Guan, Zhitong Mi, Zheng Yuan. 2022-10-12. Optimal $L^2$ extension for holomorphic vector bundles with singular hermitian metrics. https://arxiv.org/abs/2210.06026

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