Metric limits of manifolds with positive scalar curvature
Abstract
abstract: We show that any Riemannian metric conformal to the round metric on $\mathbb{S}^n$, for $n\geq 4$, arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on $\mathbb{S}^n$ in the sense of uniform convergence of Riemannian distance. In particular, non-negativity of scalar curvature is not preserved under such limits.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Advanced Differential Geometry Research
Publication details
- Journal / source
- American Journal of Mathematics
- Publisher
- Project MUSE
- Volume
- 148
- Issue
- 4
- Pages
- 901–914
- Publication date
- 1 August 2026
- Language
- EN