Monge-Ampère type equation on compact Hermitian manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914820065853440 |
|---|---|
| author | Li, Yinji Lin, Genglong Zhou, Xiangyu |
| author_facet | Li, Yinji Lin, Genglong Zhou, Xiangyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14958 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Monge-Ampère type equation on compact Hermitian manifolds Li, Yinji Lin, Genglong Zhou, Xiangyu Differential Geometry Complex Variables 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. |
| title | Monge-Ampère type equation on compact Hermitian manifolds |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2311.14958 |