https://neckpinch.com/authors/gianmichele-di-matteo/New arXiv papers by Gianmichele Di Matteo, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2606.12379/arxiv:2606.12379Wed, 10 Jun 2026 00:00:00 GMTReto Buzano, Gianmichele Di Matteo — We continue our local singularity analysis for Ricci flow initiated in ArXiv:2006.16227. Building on that framework, we study Type I singular points in general Ricci flows, without assuming any global Type I curvature bound, and prove that the scalar curvature must blow up at a Type I rate at each such point in all dimensions. As a consequence, Ricci flows with bounded scalar curvature cannot develop Type I singular points. This extends earlier results of the first author with Enders and Topping and with Mantegazza that relied on a global Type I assumption. We then adapt the same local perspective to ancient Ricci flows and analyse the curvature behaviour as time goes to negative infinity, showing in particular that every ancient Type I point exhibits scalar curvature behaviour of ancient Type I order.Ricci flowAncient solutionsSingularitiesScalar curvature