P. Burkhardt-Guim - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow

Paula Burkhardt-Guim (1) , Fanny Bastien (2) , Hugo Béchet (2)

1 Department of Mathematics [Berkeley]
2 IF - Institut Fourier

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.

Mots clés: pointwise; scalar; bounds; Ricci flow; eem2021; grenoble; curvature constraints and spaces of metrics

Mots clés: contraintes de courbures et espaces métriques

Domaines: Mathématiques [math]

Paula Burkhardt-Guim, Fanny Bastien, Hugo Béchet. P. Burkhardt-Guim - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow: Summer School 2021 - Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03322457⟩