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 $G/K$ of compact type which is invariant under a hyperpolar action on $G/K$. First, in the case of $G/K=SO(n+1)/SO(n)$, SU(n+1)/S(U(1)× U(n)), Sp(n+1)/(Sp(1)× Sp(n)) or F₄/Spin(9), we classify the shapes of translators in G/K× R given by the graphs of functions on $G/K$ which are invariant under the isotropy action K G/K. Next, in the case where $G/K$ is of higher rank, we investigate translators in G/K × R given by the graphs of functions on $G/K$ which are invariant under a hyperpolar action H G/K of cohomogeneity two.