Higher-order Ricci estimates along immortal Kähler-Ricci flows
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917361660985344 |
|---|---|
| author | Kong, Wenrui |
| author_facet | Kong, Wenrui |
| contents | We study higher-order curvature estimates along Kähler-Ricci flows on compact Kähler manifolds of intermediate Kodaira dimension. We prove that away from singular fibers, the Ricci curvature is uniformly bounded in $C^1$, the Laplacian of the Ricci curvature in $C^0$, and the scalar curvature in $C^2$. We identify a geometric obstruction to higher-order curvature bounds, whose non-vanishing causes a specific third-order derivative of the Ricci curvature to blow up at rate $e^{t/2}$. Uniform $C^k$ bounds for every $k$ hold for the Ricci curvature in the isotrivial case, and for the full Riemann curvature in the torus-fibered case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24380 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-order Ricci estimates along immortal Kähler-Ricci flows Kong, Wenrui Differential Geometry Analysis of PDEs 53E30, 53C55, 32Q15, 32W20, 35K96, 58J35 We study higher-order curvature estimates along Kähler-Ricci flows on compact Kähler manifolds of intermediate Kodaira dimension. We prove that away from singular fibers, the Ricci curvature is uniformly bounded in $C^1$, the Laplacian of the Ricci curvature in $C^0$, and the scalar curvature in $C^2$. We identify a geometric obstruction to higher-order curvature bounds, whose non-vanishing causes a specific third-order derivative of the Ricci curvature to blow up at rate $e^{t/2}$. Uniform $C^k$ bounds for every $k$ hold for the Ricci curvature in the isotrivial case, and for the full Riemann curvature in the torus-fibered case. |
| title | Higher-order Ricci estimates along immortal Kähler-Ricci flows |
| topic | Differential Geometry Analysis of PDEs 53E30, 53C55, 32Q15, 32W20, 35K96, 58J35 |
| url | https://arxiv.org/abs/2603.24380 |