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.
@article{2064,
title = {Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces},
journal = {CUBO, A Mathematical Journal},
volume = {20},
year = {2018},
doi = {10.4067/S0719-06462018000300013},
language = {en},
url = {http://dml.mathdoc.fr/item/2064}
}
Koike, Naoyuki. Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces. CUBO, A Mathematical Journal, Tome 20 (2018) . doi : 10.4067/S0719-06462018000300013. http://gdmltest.u-ga.fr/item/2064/