  We show that (a) any entire graphic self-shrinking solution to the Lagrangian
mean curvature flow in ${\mathbb C}^{m}$ with the Euclidean metric is flat; (b)
any space-like entire graphic self-shrinking solution to the Lagrangian mean
curvature flow in ${\mathbb C}^{m}$ 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 K\"ahler Ricci flow.
