https://neckpinch.com/authors/hongxin-guo/New arXiv papers by Hongxin Guo, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.37154/arxiv:2610.37154Tue, 27 Oct 2026 00:00:00 GMTHongxin Guo, Guozhi Lin — For a rotationally symmetric Ricci flow g(t)=ds²+f(s,t)²g_(Sⁿ⁻¹), n≥3, we study the scale-invariant curvature anisotropy A=1-fₛ²+ffₛₛ introduced by Angenent–Knopf. At the critical power p_*=(n-1)/(n-2), with Φ=sgn(A)|A|^(p_*/2), we prove the distributional identity (∂ₜ−Δ)|A|^(p_*) =−4/n-1 |Φₛ+(n-1)(fₛ)/fΦ|². Integration against a conjugate heat kernel gives an anisotropic entropy formula. As an application, we obtain an entropy threshold for Type-I singularities on Sⁿ: if the entropy associated with a singular-time kernel is at most 1 at an earlier regular time, every tangent flow at the corresponding singular point is a round shrinking sphere. This criterion follows from the 0/1 quantization of the singular-time anisotropic density.Ricci flowSingularitiesHeat kernelRotational symmetry & warped products