Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces

Mean curvature flows of isoparametric submanifolds in Euclidean spaces and spheres have been studied by Liu and Terng in \cite{X.CT} and \cite{X.C}. In particular, it was proved that such flows always have ancient solutions. This is also true for mean curvature flows of isoparametric hypersurfaces in hyperbolic spaces by a result of Reis and Tenenblat in \cite{S.H.T}. In this paper, we study mean curvature flows of isoparametric submanifolds in hyperbolic spaces with arbitrary codimension. In particular, we will show that they always have ancient solutions and study their limiting behaviors.