Negative holomorphic bisectional curvature of some bounded domains
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929420365725696 |
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| author | Bakkacha, Omar |
| author_facet | Bakkacha, Omar |
| contents | We prove that a bounded domain in $\mathbb{C}^n$ admitting a complete Kähler metric with negatively pinched holomorphic bisectional curvature near the boundary, admits a complete Kähler metric with negatively pinched holomorphic bisectional curvature everywhere. As a consequence we prove that strictly pseudoconvex bounded domains with $C^2$ boundary and bounded domains with squeezing function tending to 1 at every point of the boundary, admit a complete Kähler metric with negatively pinched holomorphic bisectional curvature everywhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Negative holomorphic bisectional curvature of some bounded domains Bakkacha, Omar Complex Variables Differential Geometry 32Q15, 32Q05, 32T15 We prove that a bounded domain in $\mathbb{C}^n$ admitting a complete Kähler metric with negatively pinched holomorphic bisectional curvature near the boundary, admits a complete Kähler metric with negatively pinched holomorphic bisectional curvature everywhere. As a consequence we prove that strictly pseudoconvex bounded domains with $C^2$ boundary and bounded domains with squeezing function tending to 1 at every point of the boundary, admit a complete Kähler metric with negatively pinched holomorphic bisectional curvature everywhere. |
| title | Negative holomorphic bisectional curvature of some bounded domains |
| topic | Complex Variables Differential Geometry 32Q15, 32Q05, 32T15 |
| url | https://arxiv.org/abs/2407.10295 |