Poincaré-Einstein 4-manifolds with conformally Kähler geometry
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909827132817408 |
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| author | Li, Mingyang Liu, Hongyi |
| author_facet | Li, Mingyang Liu, Hongyi |
| contents | We study 4-dimensional Poincaré-Einstein manifolds whose conformal class contains a Kähler metric. Such Einstein metrics are non-Kähler and admit a Killing field extending to the conformal infinity, and the Einstein equation reduces to a Toda-type equation. When the Killing field integrates to an $\mathbb{S}^1$-action, we formulate a Dirichlet boundary value problem and establish existence and uniqueness theory. This construction provides a non-perturbative realization of infinite-dimensional families of new Poincaré-Einstein metrics whose conformal infinities are of non-positive Yamabe type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poincaré-Einstein 4-manifolds with conformally Kähler geometry Li, Mingyang Liu, Hongyi Differential Geometry Mathematical Physics Analysis of PDEs We study 4-dimensional Poincaré-Einstein manifolds whose conformal class contains a Kähler metric. Such Einstein metrics are non-Kähler and admit a Killing field extending to the conformal infinity, and the Einstein equation reduces to a Toda-type equation. When the Killing field integrates to an $\mathbb{S}^1$-action, we formulate a Dirichlet boundary value problem and establish existence and uniqueness theory. This construction provides a non-perturbative realization of infinite-dimensional families of new Poincaré-Einstein metrics whose conformal infinities are of non-positive Yamabe type. |
| title | Poincaré-Einstein 4-manifolds with conformally Kähler geometry |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04928 |