Title: A generalization of a theorem by Calabi to the parabolic Monge-Ampere equation

Authors: Cristian E. Gutierrez and Qingbo Huang

Issue: Volume 47 (1998), Issue 4, 1459-1480

Abstract: 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 $-\infty$, and is a solution of the parabolic Monge-Amp\`ere equation $-u_t\ \text{det}\;D_x^2 u = 1$ in $\mathbb{R}^n \times (-\infty,0]$, then $u$ must be of the form of a convex quadratic polynomial in $x$ plus a linear function of $t$.