Abstract In this article, we establish an L 2 L^2 extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties for the multiplier submodule sheaves associated to such singular metrics. We solve affirmatively a question of Lempert on the preservation of Nakano semi-positivity under limit of an increasing sequence of metrics based on DengâNingâWangâZhouâs characterization of Nakano positivity.
Liu et al. (2026) studied this question.