https://neckpinch.com/authors/wenshuai-jiang/New arXiv papers by Wenshuai Jiang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2510.17060/arxiv:2510.17060Mon, 20 Oct 2025 00:00:00 GMTYiqi Huang, Wenshuai Jiang — We show that the intrinsic diameter of mean curvature flow in ℝ³ is uniformly bounded as one approaches the first singular time T. This confirms the bounded diameter conjecture of Haslhofer. In addition, we establish several sharp quantitative estimates: the second fundamental form A has uniformly bounded L¹-norm on each time slice, A belongs to the weak L³ space on the space-time region, and the singular set 𝓢 has finite 𝓗¹-Hausdorff measure. All of the results are optimal due to the marriage ring example and our results do not require any convexity assumptions on the surfaces. Furthermore, our arguments extend naturally to flows through singularities, yielding the same sharp estimates.Mean curvature flowSingularitiesWeak & singular flows https://neckpinch.com/papers/2110.12157/arxiv:2110.12157Sat, 23 Oct 2021 00:00:00 GMTWenshuai Jiang, Weimin Sheng, Huaiyu Zhang — In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon that the Ricci flow exists for a short time. We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in distributional sense provided that the initial metric is W^(1,p) for some n<p≤ ∞. As an application, we use this result to study the relation between Yamabe invariant and Ricci flat metrics. We prove that if the Yamabe invariant is nonpositive and the scalar curvature is nonnegative in distributional sense, then the manifold is isometric to a Ricci flat manifold.Ricci flowRicci-flat & Calabi–YauScalar curvature