A rigidity theorem for parabolic 2-Hessian equations

Abstract

In this paper, we consider the entire solution to the parabolic 2 2 -Hessian equation − u t σ 2 ( D 2 u ) = 1 -u_t\sigma _2(D^2 u)=1 in R n × ( − ∞ , 0 ] \mathbb {R}^n\times (-\infty ,0] . We prove a rigidity theorem for the parabolic 2 2 -Hessian equation in R n × ( − ∞ , 0 ] \mathbb {R}^n\times (-\infty ,0] by establishing Pogorelov type estimates for 2 2 -convex-monotone solutions.