https://neckpinch.com/authors/john-lott/New arXiv papers by John Lott, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.30027arxiv:2608.30027Sun, 30 Aug 2026 00:00:00 GMTJohn Lott — We determine the long-time behavior of the canonical Ricci flow on a closed three-manifold of Thurston type ℝ³, Nil, or Sol, starting from an arbitrary initial metric. In the Euclidean case, the metric g(t) converges exponentially fast to a flat metric. The Gromov–Hausdorff limit of (M,t⁻¹g(t)) is a point in the Euclidean and Nil cases, and a metric circle or a compact interval of positive length in the Sol case. In all three cases, the blowdown flows lifted to the universal cover, s⁻¹widetilde g(sτ), converge, in the pointed Cheeger–Hamilton sense, to an explicit homogeneous expanding Ricci soliton solution.Ricci flowRicci solitonsGeometrization3-manifoldsLimit spaces & RCDHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2501.12759arxiv:2501.12759Wed, 22 Jan 2025 00:00:00 GMTJohn Lott — We give biLipschitz models for the Ricci flow on some 4-manifolds (minimal surfaces of general type), exhibiting a combination of expanding and static behavior.Ricci flow4-manifoldsLong-time existence & convergenceMinimal & CMC surfacesAnalytic minimal model program https://arxiv.org/abs/2110.07551arxiv:2110.07551Thu, 14 Oct 2021 00:00:00 GMTJohn Lott — We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a Ricci flow solution.Ricci flowScalar curvature https://arxiv.org/abs/1408.2271arxiv:1408.2271Sun, 10 Aug 2014 00:00:00 GMTBruce Kleiner, John Lott — We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery parameter varies. We prove that the flow with surgery subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.Ricci flowSurgery3-manifoldsWeak & singular flows https://arxiv.org/abs/math/0605667arxiv:math/0605667Thu, 25 May 2006 00:00:00 GMTBruce Kleiner, John Lott — These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds".Ricci flowSurgery3-manifolds