https://neckpinch.com/authors/zhengnan-chen/New arXiv papers by Zhengnan Chen, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2509.13183/arxiv:2509.13183Tue, 16 Sep 2025 00:00:00 GMTZhengnan Chen — For all dimensions n≥5, let (M,g,f) be a n-dimensional shrinking gradient Ricci soliton with strictly positive isotropic curvature (PIC). Suppose furthermore that ∇²f is 2-nonnegative and the curvature tensor is WPIC1 at some point x∈ M. Then (M,g) must be a quotient of either Sⁿ or Sⁿ⁻¹×ℝ. Our result partially extends the classification result for 4-dimensional PIC shrinking Ricci solitons established in [LNW16] to highter dimensions. Combining the pinching estimates deduced in [Chen24] we also extend the result in [CL23] to dimensions n≥9. Namely that a complete ancient solution to the Ricci flow of dimension n≥9 with uniformly PIC must be weakly PIC2.Ricci flowRicci solitonsAncient solutionsCurvature pinching4-manifoldsSphere theorems