Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow

Abstract

In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ 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 $C^0$ 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 $C^0$ initial data.

arXiv comment65 pages. v3: small errors corrected. This is a post-peer-review, pre-copyedit version of an article published in Geometric and Functional Analysis. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00039-019-00514-3

References in corpus (2)

• Uniqueness and stability of Ricci flow through singularities
• Doubling a cube with positive scalar curvature

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