A Rigidity Theorem For Parabolic 2-Hessian Equations

Fully nonlinear partial differential equation is a very important branch in the field of partial differential equation.As one of the classical completely nonlinear partial differential equations,6)-Hessian equation has attracted wide attention because of its important research significance in equation,geometry and so on.In this paper,we take the parabolic 2-Hessian equation as the research object,and prove the rigidity theorem of the parabolic 2-Hessian equation by establishing the2-convex simple mediation Pogorelov type estimation of the parabolic 2-Hessian equation.This article can be divided into the following five parts for discussion.In our first part,the related research background and research status of 6)-Hessian equation are introduced,and the main theorems of this paper are given.In the second part,we mainly give the relevant basic knowledge,such as the properties of basic symmetric polynomials,the relevant knowledge of differential equations and so on,in preparation for the following research.In the third part,we mainly establish the Pogorelov type estimation of the solution of parabolic 2-Hessian equation.In the fourth part,the main theorem of this paper is proved by using the Pogorelov type estimation,and the rigidity theorem of the parabolic 2-Hessian equation is obtained under certain conditions.