https://neckpinch.com/authors/fengjiang-li/New arXiv papers by Fengjiang Li, 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/2502.16148arxiv:2502.16148Sat, 22 Feb 2025 00:00:00 GMTShu-Cheng Chang, Fengjiang Li, Chien Lin, Hongbing Qiu — In this paper, we study several properties of Sasaki-Ricci solitons as singularity models of the Sasaki-Ricci flow. First, we establish several fundamental equations for Sasaki-Ricci solitons, which enable us to derive potential estimates and prove the positivity of the scalar curvature. Then we present two criteria for the transverse rigidity of Sasaki-Ricci solitons. As essential applications, we prove that any low-dimensional Sasaki-Ricci soliton with constant scalar curvature must be Sasaki-Einstein, and that any Sasaki-Ricci soliton with harmonic Weyl tensor is a finite quotient of the sphere.Ricci flowRicci solitonsSingularitiesScalar curvatureStability & uniquenessSasakian & contact geometry 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/2406.16430arxiv:2406.16430Mon, 24 Jun 2024 00:00:00 GMTShu-Cheng Chang, Fengjiang Li, Chien Lin, Chin-Tung Wu — In this paper, we derive the uniform L^4-bound of the transverse conic Ricci curvature along the conic Sasaki-Ricci flow on a compact transverse log Fano Sasakian manifold M of dimension five and the space of leaves of the characteristic foliation is not well-formed. Then we first show that any solution of the conic Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold conic Sasaki-Ricci soliton on M_infinite which is a S^1-orbibundle over the unique singular conic Keahler-Ricci soliton on a log del Pezzo orbifold surface. As a consequence, there exists a Keahler-Ricci soliton orbifold metric on its leave space which is a log del Pezzo orbifold surface. Second, we show that the conic Sasaki-Ricci soliton is the conic Sasaki-Einstein if M is transverse log K-polystable. In summary, we have the existence theorems of orbifold Sasaki-Ricci solitons and Sasaki-Einstein metrics on a compact quasi-regular Sasakian manifold of dimension five.Ricci flowRicci solitonsEinstein metricsKähler geometryKähler–Einstein & K-stabilitySasakian & contact geometry