Randomized trial shows non-negativity of scalar curvature does not persist in manifolds with limits, suggesting new insights.
We show that any Riemannian metric conformal to the round metric on Sⁿ, for n≥ 4, arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on Sⁿ 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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Lee et al. (2026) studied this question.
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