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arXiv · 2311.14958

Monge-Ampère type equation on compact Hermitian manifolds

Yinji Li·Genglong Lin·Xiangyu Zhou
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Abstract

Given a cohomology $(1,1)$-class $\{β\}$ of compact Hermitian manifold $(X,ω)$ possessing a bounded potential and fixed a model potential $ϕ$, motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that degenerate complex Monge-Ampère equation $(β+dd^c φ)^n=e^{λφ}μ$ has a unique solution in the relative full mass class $\mathcal{E}(X,β,ϕ)$, where $μ$ is a non-pluripolar measure on $X$ and $λ\geq0$ is a fixed constant. As an application, we give an explicit description of Lelong numbers of elements in $\mathcal{E}(X,β,ϕ)$ which generalized a theorem of Darvas-Di Nezza-Lu in the Hermitian context.

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Yinji Li, Genglong Lin, Xiangyu Zhou. 2024-06-03. Monge-Ampère type equation on compact Hermitian manifolds. https://arxiv.org/abs/2311.14958

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