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arXiv · 2212.10416

Positive Scalar Curvature Meets Ricci Limit Spaces

Jinmin Wang·Zhizhang Xie·Bo Zhu·Xingyu Zhu
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Abstract

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.

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Jinmin Wang, Zhizhang Xie, Bo Zhu, Xingyu Zhu. 2024-10-24. Positive Scalar Curvature Meets Ricci Limit Spaces. https://arxiv.org/abs/2212.10416

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