Strengthened injectivity radius bounds for manifolds with positive scalar curvature
Abstract
Green's inequality shows that a compact Riemannian manifold with scalar curvature at least $n(n-1)$ has injectivity radius at most $\pi$, and that equality is achieved only for the radius 1 sphere. In this work we show how extra topological assumptions can lead to stronger upper bounds. The topologies we consider are $\mathbb{S}^2\times\mathbb{T}^{n-k-2}\times\mathbb{R}^k$ for $n\leq 7$ and $0\leq k\leq 2$ and 3-manifolds with positive scalar curvature except lens spaces $L(p,q)$ with $p$ odd. We also prove a strengthened inequality for $3$-manifolds with positive scalar curvature and large diameter. Our proof uses previous results of Gromov and Zhu.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Operator Algebra Research
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Publisher
- International Press of Boston
- Volume
- 34
- Issue
- 2
- Pages
- 603–624
- Publication date
- 1 January 2026
- Language
- EN