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arXiv · 2203.01223

Metric limits of manifolds with positive scalar curvature

Man-Chun Lee·Peter M. Topping
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Abstract

We show that any Riemannian metric conformal to the round metric on $S^n$, for $n\geq 4$, arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on $S^n$ in the sense of uniform convergence of Riemannian distance. In particular, non-negativity of scalar curvature is not preserved under such limits.

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Man-Chun Lee, Peter M. Topping. 2022-03-02. Metric limits of manifolds with positive scalar curvature. https://arxiv.org/abs/2203.01223

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