Translators invariant under hyperpolar actions

In this paper, we consider translators (for the mean curvature flow) given by a graph of a function on a symmetric space $G\mathrm{/}K$ of compact type which is invariant under a hyperpolar action on $G\mathrm{/}K$. First, in the case of $G\mathrm{/}K=SO(n+1)\mathrm{/}SO(n)$, $SU(n+1)\mathrm{/}S(U(1)\times U(n))$, $Sp(n+1)\mathrm{/}(Sp(1)\times Sp(n))$ or $F_4\mathrm{/}\mathrm{S}\mathrm{p}\mathrm{i}\mathrm{n}(9)$, we classify the shapes of translators in $G\mathrm{/}K\times \mathbb{R}$ given by the graphs of functions on $G\mathrm{/}K$ which are invariant under the isotropy action $K\curvearrowright G\mathrm{/}K$. Next, in the case where $G\mathrm{/}K$ is of higher rank, we investigate translators in $G\mathrm{/}K\times \mathbb{R}$ given by the graphs of functions on $G\mathrm{/}K$ which are invariant under a hyperpolar action $H\curvearrowright G\mathrm{/}K$ of cohomogeneity two.