Any k+1-convex-monotone solution to -u_t σ_k(D²u)=1 with quadratic growth on u(x,0) and 0<m1≤-u_t≤m2 is linear in t plus quadratic in x.
An extension of J ¨orgens-Calabi-Pogorelov theorem to parabolic Monge-Amp` re equation
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A Pogorelov estimate and a Liouville type theorem to parabolic $k$-Hessian equations
Any k+1-convex-monotone solution to -u_t σ_k(D²u)=1 with quadratic growth on u(x,0) and 0<m1≤-u_t≤m2 is linear in t plus quadratic in x.