标题： 体积守恒平均曲率流在秩一非紧对称空间中的管状流形 显示英文标题

标题： Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type

摘要： 首先，我们研究了从对称空间中紧致闭包域上的反射子流形上的一条管（具有非恒定半径）出发的保体积平均曲率流中半径函数及其梯度的演化，前提是半径函数满足某些条件。 其次，我们证明了当环境空间是非紧秩一对称空间（不是（实）双曲空间），且反射子流形是不变子流形，初始管的半径函数为径向时，管状性在流中得以保持。 此外，在这种情况下，我们还证明了流会到达不变子流形，或者在无限时间内存在，并以 $C^{\infty}$-拓扑收敛到另一个在不变子流形上的常平均曲率管。 显示英文摘要

摘要： First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space under certain condition for the radius function. Next, we prove that the tubeness is preserved along the flow in the case where the ambient space is a rank one symmetric space of non-compact type (other than a (real) hyperbolic space) and the reflective submanifold is an invariant submanifold and the radius function of the initial tube is radial. Furthermore, in this case, we prove that the flow reaches to the invariant submanifold or it exists in infinite time and converges to another tube of constant mean curvature over the invariant submanifold in the $C^{\infty}$-topology in infinite time.