On the extension of K\"ahler currents on compact complex manifolds

Jiafu Ning; Kai Pang; Haoyuan Sun; Zhiwei Wang; Xiangyu Zhou

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arXiv · 2608.01330

On the extension of K\"ahler currents on compact complex manifolds

Jiafu Ning·Kai Pang·Haoyuan Sun·Zhiwei Wang·Xiangyu Zhou

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Abstract

Let $(X,\omega)$ be a compact K\"ahler manifold and let $V\subset X$ be a closed complex submanifold. Coman-Guedj-Zeriahi proposed the problem: is every $\omega|_V$-plurisubharmonic function on $V$ the restriction of an $\omega$-plurisubharmonic function on $X$? In this paper, we solve this problem affirmatively, even for a compact Hermitian manifold.

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Jiafu Ning, Kai Pang, Haoyuan Sun, Zhiwei Wang, Xiangyu Zhou. 2026-08-02. On the extension of K\"ahler currents on compact complex manifolds. https://arxiv.org/abs/2608.01330

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