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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09203 |
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| _version_ | 1866911052757729280 |
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| author | Wang, Mingwei Yang, Xiaokui |
| author_facet | Wang, Mingwei Yang, Xiaokui |
| contents | Let $ (M,ω_g) $ be a complete Kähler manifold of complex dimension $n$. We prove that if the holomorphic sectional curvature satisfies $\mathrm{HSC} \geq 2 $, then the first eigenvalue $λ_1$ of the Laplacian on $(M,ω_g)$ satisfies $$ λ_1 \geq \frac{320(n-1)+576}{81(n-1)+144}.$$ This result is established through a new Bochner-Kodaira type identity specifically developed for holomorphic sectional curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First eigenvalue estimates on complete Kähler manifolds Wang, Mingwei Yang, Xiaokui Differential Geometry 53C55 Let $ (M,ω_g) $ be a complete Kähler manifold of complex dimension $n$. We prove that if the holomorphic sectional curvature satisfies $\mathrm{HSC} \geq 2 $, then the first eigenvalue $λ_1$ of the Laplacian on $(M,ω_g)$ satisfies $$ λ_1 \geq \frac{320(n-1)+576}{81(n-1)+144}.$$ This result is established through a new Bochner-Kodaira type identity specifically developed for holomorphic sectional curvature. |
| title | First eigenvalue estimates on complete Kähler manifolds |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2507.09203 |