https://neckpinch.com/authors/jianyu-ou/New arXiv papers by Jianyu Ou, 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 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/2411.12171arxiv:2411.12171Tue, 19 Nov 2024 00:00:00 GMTFei He, Jianyu Ou — We prove an upper bound for the dimension of the linear space of holomorphic functions with polynomial growth on gradient Kähler Ricci shrinkers with bounded curvature. The upper bound is given as a power function of the growth rate. Similar results hold for holomorphic (p, 0)-forms, and holomorphic sections of the pluri-anticanonical line bundle K_M^(−q). We also prove the existence of holomorphic sections of K_M^(−q) with polynomial growth when the Kähler Ricci shrinker is asymptotically conical, provided q is sufficiently large; as an application, we show that the Kodaira map constructed using such sections is a holomorphic embbedding into a complex projective space.Ricci solitonsKähler geometryBoundaries & non-compact 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 https://arxiv.org/abs/2401.02685arxiv:2401.02685Fri, 05 Jan 2024 00:00:00 GMTFei He, Jianyu Ou — We study polynomial growth holomorphic functions and forms on complete gradient shrinking Ricci solitons. By relating to the spectral data of the f-Laplacian, we show that the dimension of the space of polynomial growth holomorphic functions or holomorphic (p,0)-forms are finite. In particular, a sharp dimension estimate for the space of linear growth holomorphic functions was obtained. Under some additional curvature assumption, we prove an almost sharp estimate for the frequency of polynomial growth holomorphic functions, which was used to obtain dimension upper bound as a power function of the polynomial order.Ricci solitonsKähler geometryEigenvalues & spectrum https://arxiv.org/abs/2208.07101arxiv:2208.07101Mon, 15 Aug 2022 00:00:00 GMTWeixiong Mai, Jianyu Ou — In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate : any bounded harmonic function is constant on gradient shrinking Ricci solitons with constant scalar curvature. As an application, we show that the space of harmonic functions with polynomial growth has finite dimension.Ricci solitonsScalar curvature