Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow

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Appears in collection : Summer School 2021 - Curvature Constraints and Spaces of Metrics

We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from C0 initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from C0 initial data.