https://neckpinch.com/authors/xianbin-huang/New arXiv papers by Xianbin Huang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.10575/arxiv:2610.10575Mon, 05 Oct 2026 00:00:00 GMTXianbin Huang, Wancheng Zhang — In this paper, we study Ricci flows with uniformly bounded scalar curvature. On such Ricci flows we establish uniform L² Riemannian curvature bounds and L⁴ Ricci curvature bounds up to dimension 7. These estimates improves L^(2-ε) curvature bounds established by Bamler and L² curvature bounds in dimension 4 established by Bamler and Zhang. More generally, we establish uniform L² curvature bounds on n-manifolds satisfying an integral L^p Ricci curvature bound for p> n/2, a uniform volume lower bound, and a strong ε-regularity assumption. This result extends the celebrated L² curvature estimates of Jiang and Naber, which were established under pointwise two-sided Ricci curvature bounds. To overcome the lack of pointwise control, we develop an L^p adaptation of the neck decomposition theorem and establish a superconvexity estimate for the curvature on neck regions. Furthermore, we demonstrate that our structural assumptions are dynamically natural on Ricci flows with bounded scalar curvature. As an application, by combining our estimate with the a priori L^(4-ε) curvature radius bound of Ricci flow established by Bamler, we obtain uniform L² curvature bounds on Ricci flows with bounded scalar curvature of dimension n ≤ 7.Ricci flow4-manifoldsScalar curvature