A lower bound for the curvature integral under an upper curvature bound
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916844830457856 |
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| author | Fujioka, Tadashi |
| author_facet | Fujioka, Tadashi |
| contents | We prove that the integral of scalar curvature over a Riemannian manifold is uniformly bounded below in terms of its dimension, upper bounds on sectional curvature and volume, and a lower bound on injectivity radius. This is an analogue of an earlier result of Petrunin for Riemannian manifolds with sectional curvature bounded below. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11577 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A lower bound for the curvature integral under an upper curvature bound Fujioka, Tadashi Differential Geometry Metric Geometry 53B21, 53C20, 53C21, 53C23 We prove that the integral of scalar curvature over a Riemannian manifold is uniformly bounded below in terms of its dimension, upper bounds on sectional curvature and volume, and a lower bound on injectivity radius. This is an analogue of an earlier result of Petrunin for Riemannian manifolds with sectional curvature bounded below. |
| title | A lower bound for the curvature integral under an upper curvature bound |
| topic | Differential Geometry Metric Geometry 53B21, 53C20, 53C21, 53C23 |
| url | https://arxiv.org/abs/2306.11577 |