Rigidity of entire self-shrinking solutions to curvature flows

We show (a) that any entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C-n with the Euclidean metric is flat; (b) that any space-like entire graphic self-shrinking solution to the Lagrangian mean curvature flow in C-n with the pseudo-Euclidean metric is flat if the Hessian of the potential is bounded below quadratically; and (c) the Hermitian counterpart of (b) for the Kahler Ricci flow.