https://neckpinch.com/authors/chen-wang/New arXiv papers by Chen Wang, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2604.26163/arxiv:2604.26163Tue, 28 Apr 2026 00:00:00 GMTChen Wang, Guoqiang Wu — Let (M⁴, g, f) be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation Ric+∇²f= 1/2g. If its scalar curvature is 1, Cheng-Zhou proved that it is a finite quotient of ℝ²× S². In this note we present an alternative proof by analyzing the asymptotic geometry at infinity.Ricci solitons4-manifoldsScalar curvatureBoundaries & non-compact https://neckpinch.com/papers/2604.23939/arxiv:2604.23939Mon, 27 Apr 2026 00:00:00 GMTChen Wang, Guoqiang Wu — Let (Mⁿ, g, f) be an n-dimensional complete noncompact gradient shrinking Ricci soliton with the equation Ric+∇²f= 1/2g. 1. If its scalar curvature is k/2, Ricci curvature is nonnegative and sectional curvature has upper bound 1/(2(k-1)), we prove that the Ricci shrinker is isometric to a finite quotient of ℝ^(n-k)× S^k. 2. If M has constant scalar curvature R=(n-2)/2, and each level set of f has vanishing Weyl curvature, we prove that it is a finite quotient of ℝ²× Sⁿ⁻². This can be seen a generalization of Cheng-Zhou's four dimensional result to high dimension, since the level set of the potential function f has vanishing Weyl curvature automatically when n=4.Ricci solitons4-manifoldsScalar curvatureStability & uniquenessBoundaries & non-compact