# Seminars & Colloquia Calendar

Geometric Analysis Seminar

## Ricci flow and lower scalar curvature bounds of $$W^{2,2}$$ metrics in four dimensions

#### Miles Simon (Institut fuer Analysis und Numerik (IAN) Universitaet Magdeburg)

Location:  Zoom
Date & time: Tuesday, 29 March 2022 at 2:50PM - 3:50PM

Abstract: In this talk we construct solutions to Ricci DeTurck flow in four dimensions on compact manifolds which are instantaneously smooth but whose initial values are (possibly) non-smooth Riemannian metrics whose components, in smooth coordinates, belong to $$W^{2,2}$$ and are bounded from above and below. A Ricci flow related solution is constructed whose initial value is isometric in a weak sense to the initial value of the Ricci DeTurck solution. If the scalar curvature of such an initial metric is bounded from below by a constant k almost everywhere, then we show that the scalar curvature for later times is bounded from below by the same constant k.
(joint work with Tobias Lamm)