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.

中文翻译：

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关于奇异黎曼叶的平均曲率流：非紧致情况

在本文中，我们研究了封闭的广义等参叶的规则叶子作为初始基准的平均曲率流（MCF），并概括了Radeschi和第一作者的先前结果。我们证明，在有界曲率条件下，任何有限的时间奇异点都是奇异叶，并且奇异点是I型。新技术还使我们能够讨论吸引盆的存在，圆柱结构如何影响基本MCF的收敛浸入子流形，并确保紧凑流形上广义等参叶的非闭合叶的MCF收敛。