About a hundred years ago, Bernstein proved that if $f \in C^2(\mathbb{R}^2)$ and the graph of $z=f(x,y)$ is a minimal surface in $\mathbb{R}^3$, then $f$ is necessarily an affine function of $x$ and $y$. This theorem gives the characterization of entire solutions to the minimal surface equation in $\mathbb{R}^2$.
　　For Monge-Ampère equation, the following result is known; if $u \in C^4(\mathbb{R}^n)$ is a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$, then $u$ is a quadratic polynomial. This result is called "Bernstein type theorem" for Monge-Ampère equation.
　　In this talk, we shall obtain Bernstein type theorem for the so-called parabolic $k$-Hessian equation, which is a fully nonlinear parabolic PDE.
　　This talk is based on a joint work with Saori Nakamori (Hiroshima University).