Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces
In this paper, we investigate the mean curvature flows starting from all leaves of the isoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation exists in infinite time, if the foliation admits no minimal leaf, then the flow asymptotes the self-similar flow starting from another leaf, and if the foliation admits a minimal leaf (in this case, it is shown that there exists the only one minimal leaf), then the flow converges to the minimal leaf of the foliation in C∞-topology. These results give the geometric information between the leaves.
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