Christian Ketterer:
Rigidity of mean convex subsets in non-negatively curved \(RCD\) spaces and stability of mean curvature bounds
Zeit und Ort
Montag, 25.4.22, 16:15-17:15, Raum 125, Ernst-Zermelo-Str. 1
Zusammenfassung
Kasue showed the following theorem. Let \(M\) be a Riemannian manifold with non-negative Ricci curvature and mean convex boundary \(\bpartial M=N\) that is disconnected. Then it follows that \(M\) is isometric to \([0,D]\btimes N\). I present a generalization of Kasue's rigidity result for a non-smooth context. For this purpose a synthetic and stable notion of mean curvature bounded from below of subsets in \(RCD\) metric measure spaces is introduced. A consequence is a Frankel-type theorem for mean convex subsets in \(RCD\) spaces.