https://neckpinch.com/authors/weiyong-he/New arXiv papers by Weiyong He, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.38418arxiv:2610.38418Wed, 28 Oct 2026 00:00:00 GMTWeiyong He, Longhuan Yan — In this paper, we establish a new estimate on the time-derivative of pointed Nash entropy and use it to give a new proof of backward pseudolocality for Ricci flow. The proof does not rely on Bamler's compactness theorem and structure theory concerning limits of Ricci flows. Our methods also work for other reasonable geometric flows, like the G₂-Laplacian, at a scale depending on its deviation from Ricci flow and its scalar curvature.Ricci flowGeneralized & G₂ flowsPerelman entropyScalar curvatureLimit spaces & RCD https://arxiv.org/abs/2610.38408arxiv:2610.38408Wed, 28 Oct 2026 00:00:00 GMTWeiyong He, Longhuan Yan — In this paper, we give a new proof of Perelman's pseudolocality theorem for Ricci flow, which does not rely on Perelman's Harnack-type inequality. The key step is an estimate relating initial local μ-entropy to pointed Nash entropy at later spacetime points. The argument also works for other reasonable geometric flows, like the G₂-Laplacian flow, at a scale depending on its deviation from Ricci flow and its scalar curvature lower bound. As a consequence, we can also prove the quantitative rigidity results concerning pointed Nash entropy due to Hein-Naber and Bamler for such geometric flows. In the appendix, we also show that the other results in Bamler's work (arXiv:2008.07093), when suitably modified, remain valid for Laplacian flow with bounded torsion. These include log-Sobolev/Poincaré inequality for conjugate heat kernel measure, heat kernel estimates, and dependence of the pointed Nash entropy on its basepoint.Ricci flowGeneralized & G₂ flowsPerelman entropyHarnack inequalitiesHeat kernelScalar curvatureStability & uniqueness