On CMC-foliations of asymptotically flat manifolds

Abstract: In 1996, Huisken and Yau proved existence of foliations by constant mean curvature (CMC) surfaces in the asymptotic end of an asymptotically Euclidean Riemannian manifold. Their work has inspired the study of various other foliations in asymptotic ends, most notably the foliations by 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). 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). The STCMC-foliation is well-suited to define a notion of total center of mass in General Relativity.

Mathematics

Audience: researchers in the topic

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Online Seminar "Geometric Analysis"

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