Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.09573 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- Green's inequality shows that a compact Riemannian manifold with scalar curvature at least $n(n-1)$ has injectivity radius at most $π$, 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.