Positive scalar curvature meets Ricci limit spaces
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 R -fac...
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| Veröffentlicht in: | Manuscripta mathematica 2024-11, Vol.175 (3-4), p.943-969 |
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| creator | Wang, Jinmin Xie, Zhizhang Zhu, Bo Zhu, Xingyu |
| description | 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
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. |
| doi_str_mv | 10.1007/s00229-024-01596-6 |
| format | Article |
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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
R
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n
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n
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2
lines or
R
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n
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n
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R
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| identifier | ISSN: 0025-2611 |
| ispartof | Manuscripta mathematica, 2024-11, Vol.175 (3-4), p.943-969 |
| issn | 0025-2611 1432-1785 |
| language | eng |
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| source | SpringerNature Journals |
| subjects | Algebraic Geometry Calculus of Variations and Optimal Control Optimization Curvature Geometry Lie Groups Manifolds Mathematics Mathematics and Statistics Number Theory Splitting Topological Groups Upper bounds |
| title | Positive scalar curvature meets Ricci limit spaces |
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