https://neckpinch.com/authors/yifan-guo/New arXiv papers by Yifan Guo, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.19273/arxiv:2610.19273Tue, 13 Oct 2026 00:00:00 GMTYifan Guo, Xiaokang Wang — We study the α-Ricci flow (g(t),α(t)), which is a Ricci flow coupled with a harmonic 1-form heat flow, on the 2-torus M. We prove global existence for this flow as well as a Type III curvature estimate. The long-time behavior of the α-Ricci flow depends on the cohomology class [α] ∈ H¹(M,ℝ), which is invariant under the flow. If [α] is rational, then as t→∞, (M,t⁻¹g(t)) Gromov–Hausdorff converges to S¹ with length ℓ([α])/sqrt 2 where ℓ([α]) is the primitive length of [α]. On the universal cover, the rescaled flow (s⁻¹tilde g(st),tildeα(st)) smoothly converges to an expander (g^*(t),α^*(t)) on ℝ² as s→ ∞ where α^*(t) is nonzero and constant in spacetime and g^*(t) is flat and expanding in the α^* direction. If [α] is irrational, then there is a sequence sᵢ→∞ such that (M,sᵢ⁻¹g(sᵢt)) Gromov–Hausdorff converges to a point. Moreover, on the universal cover, (sᵢ⁻¹tilde g(sᵢt),tildeα(sᵢt)) smoothly converges to (g^*(t),α^*(t)).Ricci flowRicci solitonsLimit spaces & RCDLong-time existence & convergence