Monge-Amp\`ere type equation on compact Hermitian manifolds
| Autor: | Li, Yinji, Lin, Genglong, Zhou, Xiangyu |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Given a cohomology $(1,1)$-class $\{\beta\}$ of compact Hermitian manifold $(X,\omega)$ possessing a bounded potential and fixed a model potential $\phi$, motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that degenerate complex Monge-Amp\`ere equation $(\beta+dd^c \varphi)^n=e^{\lambda \varphi}\mu$ has a unique solution in the relative full mass class $\mathcal{E}(X,\beta,\phi)$, where $\mu$ is a non-pluripolar measure on $X$ and $\lambda\geq0$ is a fixed constant. As an application, we give an explicit description of Lelong numbers of elements in $\mathcal{E}(X,\beta,\phi)$ which generalized a theorem of Darvas-Di Nezza-Lu in the Hermitian context. Comment: Comments welcome |
| Databáze: | arXiv |
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