On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds
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| Format: | Preprint |
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2024
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| _version_ | 1866911827644907520 |
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| author | Li, Yinji Wang, Zhiwei Zhou, Xiangyu |
| author_facet | Li, Yinji Wang, Zhiwei Zhou, Xiangyu |
| contents | Let $(X,ω)$ be a compact Hermitian manifold of complex dimension $n$. Let $β$ be a smooth real closed $(1,1)$ form such that there exists a function $ρ\in \mbox{PSH}(X,β)\cap L^{\infty}(X)$. We study the range of the complex non-pluripolar Monge-Ampère operator $\langle(β+dd^c\cdot)^n\rangle$ on weighted Monge-Ampère energy classes on $X$. In particular, when $ρ$ is assumed to be continuous, we give a complete characterization of the range of the complex Monge-Ampère operator on the class $\mathcal E(X,β)$, which is the class of all $φ\in \mbox{PSH}(X,β)$ with full Monge-Ampère mass, i.e. $\int_X\langle (β+dd^cφ)^n\rangle=\int_Xβ^n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_03246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds Li, Yinji Wang, Zhiwei Zhou, Xiangyu Complex Variables Let $(X,ω)$ be a compact Hermitian manifold of complex dimension $n$. Let $β$ be a smooth real closed $(1,1)$ form such that there exists a function $ρ\in \mbox{PSH}(X,β)\cap L^{\infty}(X)$. We study the range of the complex non-pluripolar Monge-Ampère operator $\langle(β+dd^c\cdot)^n\rangle$ on weighted Monge-Ampère energy classes on $X$. In particular, when $ρ$ is assumed to be continuous, we give a complete characterization of the range of the complex Monge-Ampère operator on the class $\mathcal E(X,β)$, which is the class of all $φ\in \mbox{PSH}(X,β)$ with full Monge-Ampère mass, i.e. $\int_X\langle (β+dd^cφ)^n\rangle=\int_Xβ^n$. |
| title | On the Range of a class of Complex Monge-Ampère operators on compact Hermitian manifolds |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2404.03246 |