The uniqueness of Poincaré type extremal Kähler metric
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910908974891008 |
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| author | Xu, Yulun |
| author_facet | Xu, Yulun |
| contents | Let $D$ be a smooth divisor on a closed Kähler manifold $X$. Suppose that $Aut_0(D)=\{Id\}$. We prove that the Poincaré type extremal Kähler metric with a cusp singularity at $D$ is unique up to a holomorphic transformation on $X$ that preserves $D$. This generalizes Berman-Berndtson's work on the uniqueness of extremal Kähler metrics from closed manifolds to some complete and noncompact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The uniqueness of Poincaré type extremal Kähler metric Xu, Yulun Differential Geometry Analysis of PDEs 32Q15, 53C55 Let $D$ be a smooth divisor on a closed Kähler manifold $X$. Suppose that $Aut_0(D)=\{Id\}$. We prove that the Poincaré type extremal Kähler metric with a cusp singularity at $D$ is unique up to a holomorphic transformation on $X$ that preserves $D$. This generalizes Berman-Berndtson's work on the uniqueness of extremal Kähler metrics from closed manifolds to some complete and noncompact manifolds. |
| title | The uniqueness of Poincaré type extremal Kähler metric |
| topic | Differential Geometry Analysis of PDEs 32Q15, 53C55 |
| url | https://arxiv.org/abs/2504.08203 |