Oberseminare und sonstige Vorträge

Abstract: Let M be a Riemannian manifold and let G be a compact Lie group acting on M effectively and by isometries. It is well known that a lower bound of the sectional curvature of M is again a bound for the curvature of the quotient space of the action, which is an Alexandrov space of curvature bounded below. Moreover, the analogous stability property holds for metric foliations and submersions. Although this does not hold for Ricci curvature, a corresponding stability property does hold for synthetic Ricci curvature lower bounds. Specifically, for quotients of RCD*(K,N)-spaces under isomorphic compact group actions and, more generally, under metric-measure foliations and submetries. In this talk I will discuss the proof of this result as well as some geometric applications. This is joint work with Martin Kell, Andrea Mondino and Gerardo Sosa.

Abstract: I will explain what the Willmore Morse Index of unbranched Willmore spheres in Euclidean three-space is and how to compute it. A consequence of that computation is that all unbranched Willmore spheres are unstable (except for the round sphere). This talk is based on work with Jonas Hirsch.