https://neckpinch.com/authors/xu-cheng/New arXiv papers by Xu Cheng, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2605.23199/arxiv:2605.23199Fri, 22 May 2026 00:00:00 GMTXu Cheng, Franciele Conrado, Neilha Pinheiro, Detang Zhou — Let (M, g, f, τ) be a complete Ricci shrinker satisfying Ric+∇²f=g/2τ and let R denote its scalar curvature. For a confined function V on M, we obtain a lower bound for the lowest eigenvalue of the Schrödinger operator −Δ+R/4+V, expressed in terms of an integral quantity involving V and the shrinker entropy, and the equality case is characterized by the potential functions. We further generalize this estimate to complete Riemannian manifolds via Perelman's μ-functional. We also study the drifted Schrödinger operator −Δ_f+V on smooth metric measure spaces. In particular, on Ricci shrinkers, we derive a lower bound for its lowest eigenvalue, with equality if and only if V is affine.Ricci solitonsScalar curvatureLimit spaces & RCDEigenvalues & spectrum https://neckpinch.com/papers/2203.14916/arxiv:2203.14916Mon, 28 Mar 2022 00:00:00 GMTXu Cheng, Ernani Ribeiro, Detang Zhou — In this article, we investigate the geometry of 4-dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a 4-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.Ricci solitons4-manifolds