Asymptotics of small eigenvalues on degenerations of Kähler manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913103819571200 |
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| author | Cao, Junyu |
| author_facet | Cao, Junyu |
| contents | We derive the exact asymptotic rates of the small eigenvalues of the Laplacian on one-parameter degenerations of compact Kähler manifolds equipped with induced background metrics. This generalizes a recent result of Dai and Yoshikawa to higher dimensions. To achieve this, we combine Li's uniform Skoda inequality with the method of auxiliary Monge-Ampère equations, introduced by Guo--Phong--Song--Sturm--Tong and adapted by Guedj--Tô. As an application, we establish estimates for degenerations of compact Kähler manifolds with reducible singular fibers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08023 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotics of small eigenvalues on degenerations of Kähler manifolds Cao, Junyu Differential Geometry Algebraic Geometry Complex Variables 58J50, 32Q15, 35P15, 32W20, 32U05, 14D06, 53C55 We derive the exact asymptotic rates of the small eigenvalues of the Laplacian on one-parameter degenerations of compact Kähler manifolds equipped with induced background metrics. This generalizes a recent result of Dai and Yoshikawa to higher dimensions. To achieve this, we combine Li's uniform Skoda inequality with the method of auxiliary Monge-Ampère equations, introduced by Guo--Phong--Song--Sturm--Tong and adapted by Guedj--Tô. As an application, we establish estimates for degenerations of compact Kähler manifolds with reducible singular fibers. |
| title | Asymptotics of small eigenvalues on degenerations of Kähler manifolds |
| topic | Differential Geometry Algebraic Geometry Complex Variables 58J50, 32Q15, 35P15, 32W20, 32U05, 14D06, 53C55 |
| url | https://arxiv.org/abs/2605.08023 |