The Kähler-Ricci soliton on bounded pseudoconvex domains
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918444251742208 |
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| author | Sha, Zehao |
| author_facet | Sha, Zehao |
| contents | In this paper, we study Kähler-Ricci solitons on bounded pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ boundary. Under suitable assumptions, we prove that such solitons must be Kähler-Einstein. Building on Huang and Xiao's resolution of Cheng's conjecture, we further establish an analogous result for Bergman Kähler-Ricci solitons. Several model domains are presented to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Kähler-Ricci soliton on bounded pseudoconvex domains Sha, Zehao Complex Variables Differential Geometry 53C55, 32Q02 In this paper, we study Kähler-Ricci solitons on bounded pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ boundary. Under suitable assumptions, we prove that such solitons must be Kähler-Einstein. Building on Huang and Xiao's resolution of Cheng's conjecture, we further establish an analogous result for Bergman Kähler-Ricci solitons. Several model domains are presented to illustrate our results. |
| title | The Kähler-Ricci soliton on bounded pseudoconvex domains |
| topic | Complex Variables Differential Geometry 53C55, 32Q02 |
| url | https://arxiv.org/abs/2412.03345 |