Frobenius integrability of certain $p$-forms on singular spaces by Cao, Junyan, Höring, Andreas

“…Demailly proved that on a smooth compact Kähler manifold the distribution defined by a holomorphic $p$-form with values in an anti-pseudoeffective line bundle is always integrable. …”
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Optimal $L^2$ Extensions of Openness Type and Related Topics by Xu, Wang, Zhou, Xiangyu

“…We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels. …”
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