Log continuity of solutions of complex Monge-Ampère equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910815593955328 |
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| author | Do, Hoang-Son Vu, Duc-Viet |
| author_facet | Do, Hoang-Son Vu, Duc-Viet |
| contents | Let $X$ be a compact Kähler manifold whose anticanonical cohomology class is semipositive. Let $L$ be a big and semi-ample line bundle on $X$ and $α$ be the Chern class of $L$. We give a sufficient condition ensuring that the solution of the complex Monge-Ampère equations in $α$ with $L^p$ right-hand side ($p>1$) is $\log^M$-continuous for every constant $M>0$. As an application, we show that every singular Ricci-flat metric in a semi-ample integral class in a projective Calabi-Yau surface $X$ is globally $\log^M$-continuous with respect to a smooth metric on $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04128 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Log continuity of solutions of complex Monge-Ampère equations Do, Hoang-Son Vu, Duc-Viet Complex Variables Analysis of PDEs Differential Geometry Let $X$ be a compact Kähler manifold whose anticanonical cohomology class is semipositive. Let $L$ be a big and semi-ample line bundle on $X$ and $α$ be the Chern class of $L$. We give a sufficient condition ensuring that the solution of the complex Monge-Ampère equations in $α$ with $L^p$ right-hand side ($p>1$) is $\log^M$-continuous for every constant $M>0$. As an application, we show that every singular Ricci-flat metric in a semi-ample integral class in a projective Calabi-Yau surface $X$ is globally $\log^M$-continuous with respect to a smooth metric on $X$. |
| title | Log continuity of solutions of complex Monge-Ampère equations |
| topic | Complex Variables Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2312.04128 |