论文标题
对称空间和平均曲率流的极性叶面
Polar foliations on symmetric spaces and the mean curvature flow
论文作者
论文摘要
在本文中，我们研究了简单地连接的具有非负曲率的对称空间的极性叶子。我们将证明所有这些叶子都是由Heintze，Liu和Olmos定义的等法。我们还将证明一种分裂的定理，该定理将这种叶子的研究减少到紧凑的对称空间中的极性叶面。此外，我们将表明，在这种叶子中，定期叶子的曲率流的解决方案始终是古老的解决方案。这将刘和terng的一部分概括为球体中等距亚策略的平均曲率流。
In this paper, we study polar foliations on simply connected symmetric spaces with non-negative curvature. We will prove that all such foliations are isoparametric as defined by Heintze, Liu and Olmos. We will also prove a splitting theorem which reduces the study of such foliations to polar foliations in compact simply connected symmetric spaces. Moreover, we will show that solutions to mean curvature flow of regular leaves in such foliations are always ancient solutions. This generalizes part of the results of Liu and Terng for the mean curvature flow of isoparametric submanifolds in spheres.
