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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.09573 |
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| _version_ | 1866912802085535744 |
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| author | Richard, Thomas |
| author_facet | Richard, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strengthened injectivity radius bounds for manifolds with positive scalar curvature Richard, Thomas Differential Geometry 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. |
| title | Strengthened injectivity radius bounds for manifolds with positive scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2404.09573 |