Scalar curvature bounds and rigidity of Ricci shrinkers
Jianyu Ou, Guoqiang Wu
Abstract
We prove that a complete noncompact gradient shrinking Ricci soliton of dimension at least two is a finite quotient of an Einstein cylinder if its scalar curvature is bounded below by the cylindrical value. The corresponding pointwise strict bound implies compactness. We also establish one-endedness criteria using curvature information at critical points of the potential, including degenerate ones, and obtain sharp one-endedness and rigidity results under global Ricci norm bounds.
Create a lesson
Related papers
Construction of Transverse Metrics from Transversely Elliptic Operators on Foliated Manifolds
Wenran Liu
Interlacing of the Volume and Half-Volume Spectra
Xiaoxiang Jiao, Hangyue Zhu
On the anisotropic mean curvature flow in the Gaussian space
Di Zhang
On strongly convex Kähler--Berwald manifolds
Xiaoshu Ge
Trans-Sasakian space forms
Prachi, Mukut Mani Tripathi
Rigidity and Classification of Manifolds with Maximal Boundary Static Kernels
Hongyi Sheng, Caihong Yi