https://neckpinch.com/authors/wenqi-li/New arXiv papers by Wenqi 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/2610.11935arxiv:2610.11935Thu, 08 Oct 2026 00:00:00 GMTMatheus Horácio, Wenqi Li, Jianyu Ou, Guoqiang Wu, Detang Zhou — Let (M^(2m),g,f,J) be a complete nonsteady gradient Kähler-Ricci soliton satisfying Ric+∇² f=λg, λ≠ 0. We prove that constant scalar curvature forces the soliton to be rigid. More precisely, the universal cover splits holomorphically and isometrically as N^(2k)×ℂ^(m-k), where N^(2k) is Kähler-Einstein with Ric_(g_N)=λg_N. In the shrinking case the quotient is trivial; in the normalization λ=1/2 one has R≡ k. The Kähler result rests on a Riemannian rigidity criterion. On a complete nonsteady gradient Ricci soliton, if 𝓛_∇fRic is nonnegative or nonpositive everywhere, then it vanishes and the soliton is rigid; no assumption on the scalar curvature is needed. Along the Ricci flow generated by the soliton, this means that a Ricci tensor that is monotone in time is constant in time, and that this forces rigidity. We also give a direct proof that the pinching 0≤Ric≤λg forces constant scalar curvature and radial flatness, yielding the rigidity conclusion through the Petersen-Wylie characterization. The proof combines a weighted cutoff argument with a partial Codazzi symmetry for the Ricci endomorphism.Ricci flowRicci solitonsKähler–Ricci solitonsEinstein metricsCurvature pinchingKähler geometryScalar curvatureStability & uniquenessKähler–Einstein & K-stability https://arxiv.org/abs/2609.36418arxiv:2609.36418Tue, 29 Sep 2026 00:00:00 GMTWenqi Li, Jianyu Ou, Guoqiang Wu, Detang Zhou — Let (M^(2m),g,f,J) be a complete gradient Kähler–Ricci shrinker satisfying Ric+∇² f=1/2 g. We prove that if the scalar curvature is constant, then the soliton is rigid. More precisely, there exists an integer k∈\0,…,m\ such that R≡ k and (M^(2m),g,J)≅ bigl(N^(2k)×ℂ^(m-k), g_N+g_Euc,J_N⊕ J₀bigr), where (N^(2k),g_N,J_N) is Kähler–Einstein and Ric_(g_N)=1/2 g_N. As part of the proof, we establish a Riemannian rigidity criterion: for a complete nonsteady gradient Ricci soliton with constant scalar curvature, the condition 𝓛_∇fRic=0 implies radial flatness and hence rigidity.Ricci solitonsEinstein metricsKähler geometryScalar curvatureStability & uniquenessKähler–Einstein & K-stability