标题： 单参数对称空间中管状结构的保体积均曲率流 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，我们研究从反射子流形在对称空间中的紧致闭区域上的非常数半径的管状结构出发，在体积保持的平均曲率流中半径函数及其梯度的演化。 接下来，我们证明在环境空间为非紧型单李群对称空间（除实双曲空间外）且反射子流形为不变子流形，初始管状结构的半径函数为径向的情况下，管状性在流中被保持。 此外，在这种情况下，我们证明流会达到不变子流形，或者在无限时间内存在并收敛到不变子流形上的常平均曲率管状结构，在无限时间内的$C^{\infty}$-拓扑中。 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.