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.