A Rigidity theorem for parabolic 2-Hessian equations

Abstract

In this paper, we consider the entire solutions to the parabolic $2$-Hessian equations of the form $-u_t\ddot{I}{ƒ}_2(D^{2}u)=1$ in ${\mathbb{R}}^n\times (-\infty ,0]$. We prove some rigidity theorems for the parabolic $2$-Hessian equations in ${\mathbb{R}}^n\times (-\infty ,0]$ by establishing Pogorelov type estimates for $2$-convex-monotone solutions of the parabolic $2$-Hessian equations.