https://neckpinch.com/authors/zhuo-peng/New arXiv papers by Zhuo Peng, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.18364arxiv:2610.18364Tue, 13 Oct 2026 00:00:00 GMTShaochuang Huang, Zhuo Peng — In this paper, we prove a uniform pseudolocality theorem for smooth complete Ricci flows whose initial metrics have Ricci curvature bounded below and uniformly positive injectivity radius. No a priori curvature bound is assumed on the flow. As a consequence, we obtain strong uniqueness for smooth complete Ricci flows from a complete metric with the above geometric bounds. We also prove that every smooth complete Ricci flow from a complete Ricci-flat metric with uniformly positive injectivity radius is stationary. The same conclusion holds for any complete flat initial metric. In particular, we give an affirmative answer to Chen's question on the strong uniqueness of Ricci flow from Euclidean space in every dimension.Ricci flowRicci-flat & Calabi–YauStability & uniqueness https://arxiv.org/abs/2610.08233arxiv:2610.08233Tue, 06 Oct 2026 00:00:00 GMTShaochuang Huang, Zhuo Peng — In this paper, we study strong uniqueness for smooth instantaneously complete Chern-Ricci flows on noncompact complex manifolds. Under suitable reference metric and positivity assumptions, we establish strong uniqueness for initial Hermitian metrics which are Kähler outside a compact set. The initial metric may be incomplete, and no curvature, metric comparison, or growth bounds are imposed on the evolving solutions. In particular, we obtain strong uniqueness from complete initial metrics in this class with bounded Chern-Ricci curvature. We also prove stationarity of flows from the Euclidean metric on ℂⁿ and uniqueness of the instantaneously complete flow from the Euclidean metric on the complex unit ball for all positive time. Finally, on complex surfaces, we show that a Ricci flow remaining Hermitian for a fixed complex structure is Kähler at all times if it is Kähler at one time, and derive a corresponding strong uniqueness result for Ricci flows in this class.Ricci flowGeneralized & G₂ flowsKähler geometryStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2609.13938arxiv:2609.13938Sat, 12 Sep 2026 00:00:00 GMTShaochuang Huang, Zhuo Peng — In this note, we study volume comparison for 3-manifolds with 2-Ricci curvature lower bound. We establish monotonicity and rigidity for geodesic sphere area and ball volume, and derive the pointed Gromov-Hausdorff precompactness under a uniform lower bound on the conjugate radius for 3-manifolds with 2-Ricci curvature lower bound. We also discuss the almost preservation of 2-Ricci curvature lower bound and the local non-collapsing propagation along Ricci flow. Finally, we point out a topological rigidity result on nonnegative scalar curvature.Ricci flow(Non)collapsing3-manifoldsScalar curvatureLimit spaces & RCDStability & uniqueness https://arxiv.org/abs/2605.10837arxiv:2605.10837Mon, 11 May 2026 00:00:00 GMTHongting Ding, Shaochuang Huang, Zhuo Peng — In this paper, we study 4-dimensional complete noncompact manifolds (M,g) satisfying Rm(g) ∈C_(η,μ) via Ricci flow. Under the additional assumption of maximal volume growth, we prove topological and geometric gap theorems. We also study 4-dimensional complete manifolds satisfying a lower bound with respect to C_(η,μ) and obtain regularity results for Gromov-Hausdorff limits of complete volume non-collapsed manifolds satisfying such curvature lower bounds.Ricci flow(Non)collapsing4-manifoldsLimit spaces & RCDBoundaries & non-compact https://arxiv.org/abs/2509.05802arxiv:2509.05802Sat, 06 Sep 2025 00:00:00 GMTShaochuang Huang, Zhuo Peng — In this note, we give a diffeomorphism (to ℝⁿ) criterion via long-time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in [Manifolds with small curvature concentration, Ann. PDE, 2024] by Chan, Lee and the first named author and [Removing scalar curvature assumption for Ricci flow smoothing, Bull. Lond. Math. Soc., 2025] by A. Martens about manifolds with small curvature concentration can be improved to diffeomorphism in dimension 4.Ricci flowScalar curvature