  We consider a volume preserving curvature evolution of surfaces in an
asymptotically Euclidean initial data set with positive ADM-energy. The speed
is given by a nonlinear function of the mean curvature which generalizes the
spacetime mean curvature recently considered by Cederbaum-Sakovich. Following a
classical approach by Huisken-Yau, we show that the flow starting from suitably
round initial surfaces exists for all times and converges to a constant
(spacetime) curvature limit. This provides an alternative construction of the
ST-CMC foliation by Cederbaum-Sakovich and has applications in the definition
of center of mass of an isolated system in General Relativity.
