A Rigidity theorem for parabolic 2-Hessian equations

Yan He; Cen Pan; Ni Xiang

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arXiv · 1906.06682

A Rigidity theorem for parabolic 2-Hessian equations

Yan He·Cen Pan·Ni Xiang

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Abstract

In this paper, we consider the entire solutions to the parabolic $2$-Hessian equations of the form $-u_t\sigma_2(D^2 u)=1$ 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.

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Yan He, Cen Pan, Ni Xiang. 2019-06-16. A Rigidity theorem for parabolic 2-Hessian equations. https://arxiv.org/abs/1906.06682

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