https://neckpinch.com/authors/yuanyuan-qu/New arXiv papers by Yuanyuan Qu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.37151arxiv:2610.37151Tue, 27 Oct 2026 00:00:00 GMTFengjiang Li, Wenqi Li, Jianyu Ou, Yuanyuan Qu, Guoqiang Wu, Detang Zhou — Let (Mⁿ,g,f) be a complete connected shrinking gradient Ricci soliton with constant scalar curvature, satisfying Ric+∇²f=1/2g. We prove that if the focal set of f is totally geodesic, then M is rigid. Equivalently, its universal cover is a product of a compact Einstein manifold and a Euclidean space.Ricci solitonsEinstein metricsScalar curvatureStability & uniqueness https://arxiv.org/abs/2608.20040arxiv:2608.20040Thu, 20 Aug 2026 00:00:00 GMTFengjiang Li, Yuanyuan Qu, Guoqiang Wu — Let (Mⁿ, g, f) be a complete shrinking gradient Ricci soliton with constant scalar curvature. Under the assumptions that (i) Ric ≥ frac∇_∇fRicf on M∖ D, where D is a compact set over M; (ii) (Mⁿ, g, f) smoothly converges to ℝ² × Sⁿ⁻², we conclude that (Mⁿ, g, f) is isometric to ℝ² × Sⁿ⁻². Notably, condition (i) is weaker than the radial flatness condition in.Ricci solitonsScalar curvatureStability & uniqueness https://arxiv.org/abs/2506.00887arxiv:2506.00887Sun, 01 Jun 2025 00:00:00 GMTFengjiang Li, Jianyu Ou, Yuanyuan Qu, Guoqiang Wu — Suppose (M, g, f) is a 5-dimensional complete shrinking gradient Ricci soliton with R=1. If it has bounded curvature, we prove that it is a finite quotient of ℝ³× S².Ricci solitonsStability & uniqueness https://arxiv.org/abs/2411.10712arxiv:2411.10712Sat, 16 Nov 2024 00:00:00 GMTFengjiang Li, Jianyu Ou, Yuanyuan Qu, Guoqiang Wu — Let (M, g, f) be a 5-dimensional complete noncompact gradient shrinking Ricci soliton with the equation Ric+∇²f= λg, where Ric is the Ricci tensor and ∇²f is the Hessian of the potential function f. We prove that it is a finite quotient of ℝ²× S³ if M has constant scalar curvature R=3 λ.Ricci solitonsScalar curvatureStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2411.06395arxiv:2411.06395Sun, 10 Nov 2024 00:00:00 GMTJianyu Ou, Yuanyuan Qu, Guoqiang Wu — Suppose (Mⁿ, g, f) is a complete shrinking gradient Ricci soliton. We give several rigidity results under some natural conditions, generalizing the results in. Using maximum principle, we prove that shrinking gradient Ricci soliton with constant scalar curvature R=1 is isometric to a finite quotient of ℝ²× S², giving a new proof of the main results of Cheng-Zhou.Ricci solitonsScalar curvatureStability & uniqueness