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On CMC-foliations of asymptotically Euclidean manifolds
9.1.2020, 16:15 - 17:15
Speaker:Prof. Dr. Carla Cederbaum, Fachbereich Mathematik, Universität Tübingen
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerGras Geo Map
Organizer:Mathematisches Institut
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 Sakovich). This STCMC-foliation is well-suited to define the center of mass of an isolated system in General Relativity and thereby answers some previously open questions of relevance in General Relativity.
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