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arXiv · 2603.24380

Higher-order Ricci estimates along immortal K\"ahler-Ricci flows

Wenrui Kong
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Abstract

We study higher-order curvature estimates along K\"ahler-Ricci flows on compact K\"ahler 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.

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Wenrui Kong. 2026-03-25. Higher-order Ricci estimates along immortal K\"ahler-Ricci flows. https://arxiv.org/abs/2603.24380

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