Solitons of the spacelike mean curvature flow in generalized Robertson-Walker spacetimes (Q6163761)

The authors study solitons of the space-like mean curvature flow in a generalized Robertson-Walker (GRW) spacetime \[\bar M=I\times M,\quad \bar g=-(dt)^2+f^2(t)g.\] They prove nonexistence for solitons with bounded second fundamental form and hyperbolic angle function. Special attention is given to warping functions satisfying the condition \[(\log f)''\leq \gamma ((\log f)')^2, \quad \gamma\geq 0,\] for which several uniqueness and nonexistence results are obtained. Several classes of classical spacetimes are considered in detail. New Calabi-Bernstein type results are established.