Translators invariant under hyperpolar actions

Abstract

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 × 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 × given by the graphs of functions on G/K which are invariant under a hyperpolar action H ↷ G/K of cohomogeneity two.