In three dimensions, infimum scalar curvature of a perturbed metric is at most the reference value at the origin plus C times the C0 norm to the power 1/2, for sufficiently small perturbations.
Stability of Euclidean 3-space for the positive mass theorem.Inventiones math- ematicae, 239(1):287–319, 2025
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Quantification of $C^0$ Convergence in Dimension Three
In three dimensions, infimum scalar curvature of a perturbed metric is at most the reference value at the origin plus C times the C0 norm to the power 1/2, for sufficiently small perturbations.