On mean curvature flow of singular Riemannian foliations: Noncompact cases |
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Affiliation: | 1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508 090 São Paulo, Brazil;2. Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09.210-170, Santo André, Brazil |
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Abstract: | In this paper we investigate the mean curvature flow (MCF) of a regular leaf of a closed generalized isoparametric foliation as initial datum, generalizing previous results of Radeschi and the first author. We show that, under bounded curvature conditions, any finite time singularity is a singular leaf, and the singularity is of type I. The new techniques also allow us to discuss the existence of basins of attraction, how cylinder structures can affect convergence of basic MCF of immersed submanifolds and assure convergence of MCF of non-closed leaves of generalized isoparametric foliation on compact manifold. |
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Keywords: | Isoparametric submanifolds Singular Riemannian foliations Mean curvature flow |
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