Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces

  • Naoyuki Koike Department of Mathematics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka Shinjuku-ku, Tokyo 162-8601, Japan.
Keywords: error function based activation function, multivariate quasi-interpolation neural network approximation, Kantorovich-Shilkret type operator

Abstract

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.

References

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Published
2019-03-15
How to Cite
Koike, N. (2019). Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces. CUBO, A Mathematical Journal, 20(3), 13–29. https://doi.org/10.4067/S0719-06462018000300013