## <font color="red"> (FÄLLT WEGEN KRANKHEIT AUS)</font> |

## Carla Cederbaum (U Tübingen) |

## Thursday, 2023-11-09 15:00 |

Three-dimensional Riemannian manifolds are called asymptotically Euclidean if, outside a compact set, they are diffeomorphic to the exterior region of a ball in Euclidean space, and if the Riemannian metric converges to the Euclidean metric as the Euclidean radial coordinate $r$ tends to infinity. In 1996, Huisken and Yau proved existence of a foliation by constant mean curvature (CMC) surfaces in the asymptotic end of an asymptotically Euclidean Riemannian three-manifold. Their work has inspired the study of various other foliations in asymptotic ends, most notably the foliations by constrained Willmore surfaces (Lamm—Metzger—Schulze) and by constant expansion/null mean curvature surfaces in the context of asymptotically Euclidean initial data sets in General Relativity (Metzger, Nerz). After a rather extensive introduction of the central concepts and ideas, I will present a new foliation by constant spacetime mean curvature surfaces (STCMC), also in the context of asymptotically Euclidean initial data sets in General Relativity (joint work with Anna Sakovich). This STCMC-foliation is well-suited to consistently define the center of mass of an isolated system in General Relativity and thereby answers some previously open questions of relevance in General Relativity. At the end, I will touch upon subtle convergence issues for the center of mass (joint work with Christopher Nerz and with Melanie Graf and Jan Metzger). |