2015/01/07 by Giovanni Catino, Paolo Mastrolia, Dario D. Monticelli +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Corollary #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Ricci curvature #Riemann curvature tensor #Riemannian manifold #Scalar (mathematics) #Scalar curvature #Soliton #math.DG
paper · pdf · doi:10.2140/gt.2016.20.2665
published as Geom. Topol. 20 (2016) 2665-2685
arxiv created 2015/01/07 · openalex publication_date 2016/10/07 · arxiv updated 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. In this paper we prove new classification results for nonnegatively curved gradient expand-ing and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalar curvature of the underlying Riemannian manifold. In particular we show that the only complete expanding solitons with nonnegative sectional curvature and integrable scalar curvature are quotients of the Gaussian soliton, while in the steady case we prove rigidity results under sharp integral scalar curvature decay. As a corollary, we obtain that the only three dimensional steady solitons with less than quadratic volume growth are quotients of R × Σ2, where Σ2 is Hamilton’s cigar. 1. Introduction and