Minimal Degrees, Volume Growth, and Curvature Decay on Complete Kähler Manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908992503021568 |
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| author | Shi, Yuang |
| author_facet | Shi, Yuang |
| contents | We consider noncompact complete Kähler manifolds with nonnegative bisectional curvature. Our main results are: 1. Precise relations among refined minimal degree of polynomial growth holomorphic functions and holomorphic volume forms, $\operatorname{AVR}$ (asymptotic volume ratio) and $\operatorname{ASCD}$ (average of scalar curvature decay) are established. 2. The Lyapunov asymptotic behavior of the Kähler-Ricci flow can be described in terms of polynomial growth holomorphic functions. This provides a unifying perspective that bridges the two distinct proofs of Yau's uniformization conjecture by Liu and Chau-Lee-Tam. These resolve two conjectures made by Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal Degrees, Volume Growth, and Curvature Decay on Complete Kähler Manifolds Shi, Yuang Differential Geometry We consider noncompact complete Kähler manifolds with nonnegative bisectional curvature. Our main results are: 1. Precise relations among refined minimal degree of polynomial growth holomorphic functions and holomorphic volume forms, $\operatorname{AVR}$ (asymptotic volume ratio) and $\operatorname{ASCD}$ (average of scalar curvature decay) are established. 2. The Lyapunov asymptotic behavior of the Kähler-Ricci flow can be described in terms of polynomial growth holomorphic functions. This provides a unifying perspective that bridges the two distinct proofs of Yau's uniformization conjecture by Liu and Chau-Lee-Tam. These resolve two conjectures made by Yang. |
| title | Minimal Degrees, Volume Growth, and Curvature Decay on Complete Kähler Manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.01263 |