Metric limits of manifolds with positive scalar curvature

Man-Chun Lee; Peter M. Topping

Metric limits of manifolds with positive scalar curvature

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arxiv 2203.01223 v3 pith:VTL26EVS submitted 2022-03-02 math.DG math.MG

Man-Chun Lee , Peter M. Topping This is my paper · ORCID

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keywords curvaturemetricriemannianscalarlimitspositivearisesconformal

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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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Codimension 2 drawstrings with scalar curvature lower bounds
math.DG 2025-01 conditional novelty 7.0 of 10

Kazaras and Xu construct drawstring metrics along arbitrary codimension-2 submanifolds with scalar curvature almost bounded below, yielding new collapsed limits and a claimed but flawed Llarull counterexample.

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