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.
Comparison theorems for three-dimensional manifolds with scalar curvature bound
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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.