Degenerate complex Monge-Ampère equations on some compact Hermitian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910292784447488 |
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| author | Salouf, Mohammed |
| author_facet | Salouf, Mohammed |
| contents | Let $X$ be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan-Li. Given a semipositive form $θ$ with positive volume, we define the Monge-Ampère operator for unbounded $θ$-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge-Ampère equations in this context, extending recent results of Tosatti-Weinkove, Kolodziej-Nguyen, Guedj-Lu and many others who treat bounded solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Degenerate complex Monge-Ampère equations on some compact Hermitian manifolds Salouf, Mohammed Complex Variables 32W20, 32U05, 32Q15, 35A23 Let $X$ be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan-Li. Given a semipositive form $θ$ with positive volume, we define the Monge-Ampère operator for unbounded $θ$-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge-Ampère equations in this context, extending recent results of Tosatti-Weinkove, Kolodziej-Nguyen, Guedj-Lu and many others who treat bounded solutions. |
| title | Degenerate complex Monge-Ampère equations on some compact Hermitian manifolds |
| topic | Complex Variables 32W20, 32U05, 32Q15, 35A23 |
| url | https://arxiv.org/abs/2401.03440 |