Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908626827870208 |
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| author | Alehyane, Omar Lu, Chinh H. Salouf, Mohammed |
| author_facet | Alehyane, Omar Lu, Chinh H. Salouf, Mohammed |
| contents | Given a compact complex manifold $X$, we study the existence and the uniqueness of weak solutions to degenerate Monge-Ampère equations on $X$ with prescribed singularities when the reference form is semipositive and big, while the right hand side is a non-pluripolar positive Radon measure. This generalizes our previous work to more general hermitian manifolds and also to the case of solutions with prescribed singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds Alehyane, Omar Lu, Chinh H. Salouf, Mohammed Complex Variables 32W20, 32U05, 32Q15, 35A23 Given a compact complex manifold $X$, we study the existence and the uniqueness of weak solutions to degenerate Monge-Ampère equations on $X$ with prescribed singularities when the reference form is semipositive and big, while the right hand side is a non-pluripolar positive Radon measure. This generalizes our previous work to more general hermitian manifolds and also to the case of solutions with prescribed singularities. |
| title | Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds |
| topic | Complex Variables 32W20, 32U05, 32Q15, 35A23 |
| url | https://arxiv.org/abs/2511.02339 |