Positive Scalar Curvature Meets Ricci Limit Spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910665202991104 |
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| author | Wang, Jinmin Xie, Zhizhang Zhu, Bo Zhu, Xingyu |
| author_facet | Wang, Jinmin Xie, Zhizhang Zhu, Bo Zhu, Xingyu |
| contents | We investigate the influence of uniformly positive scalar curvature on the size of a non-collapsed Ricci limit space coming from a sequence of $n$-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. We prove that such a limit space splits at most $n-2$ lines or $\mathbb{R}$-factors. When this maximal splitting occurs, we obtain a uniform upper bound on the diameter of the non-splitting factor. Moreover, we obtain a volume gap estimate and a volume growth order estimate of geodesic balls on such manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10416 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Positive Scalar Curvature Meets Ricci Limit Spaces Wang, Jinmin Xie, Zhizhang Zhu, Bo Zhu, Xingyu Differential Geometry Metric Geometry 53C21, 53C23 We investigate the influence of uniformly positive scalar curvature on the size of a non-collapsed Ricci limit space coming from a sequence of $n$-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. We prove that such a limit space splits at most $n-2$ lines or $\mathbb{R}$-factors. When this maximal splitting occurs, we obtain a uniform upper bound on the diameter of the non-splitting factor. Moreover, we obtain a volume gap estimate and a volume growth order estimate of geodesic balls on such manifolds. |
| title | Positive Scalar Curvature Meets Ricci Limit Spaces |
| topic | Differential Geometry Metric Geometry 53C21, 53C23 |
| url | https://arxiv.org/abs/2212.10416 |