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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)

Zoom link:
Meeting ID: 979 5349 0430
Password: 515087

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