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Monge-Ampére type equation for the Nakano positive curvature tensor of holomorphic vector bundles

Published 9 Jan 2025 in math.DG and math.AP | (2501.05352v1)

Abstract: For any Hermitian holomorphic vector bundle with Nakano positive curvature tensor, Demailly introduced a Monge-Amp\'ere type equation. When the rank of the bundle is $1$, it becomes the usual Monge-Amp\'ere equation. In this paper, we solve this equation in the conformal class of a Nakano positive Hermitian metric.

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