We prove that if the function u = u(x, t), convex in x and nonincreasing in
t, has time derivative bounded away from 0 and -infinity, and is a solutio
n of the parabolic Monge-Ampere equation -u(t)detD(x)(2)u = 1 in R-n x (-in
finity,0), then u must be of the form a convex quadratic polynomial in x pl
us a linear function of t.