On CMC-foliations of asymptotically flat manifolds
Carla Cederbaum (Tuebingen)
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). T
he STCMC-foliation is well-suited to define a notion of total center
of mass in General Relativity.