爱因斯坦流形中超曲面的平均曲率流(英文)

MEAN CURVATURE FLOW OF HYPERSURFACES IN EINSTEINNIAN MANIFOLD

本文证明了一个拼嵌的爱因斯坦流形中的任何超曲面在沿其平均曲率向量演化时，如果初始超曲面满足保持其截曲率均为正的某些条件，则在有限时间内超曲面将收缩成一点。利用Ｈａｍｉｌｔｏｎ和Ｈｕｉｓｋｅｎ创造的许多热流方法，我们在未假设初始超曲面必须是凸的情况下证明了此一般结果。

It is shown that any hypersurface M 0 in a pinched Einsteinnian manifold N n+1 satisfying some conditions thich forces the sectional curvature of M 0 to be positive will contract a single point in finite time during the evolution of the mean curvature. Using many of the heat flow methods developed by Hamilton and Huisken, we prove this general result without assuming convexity for the initial hypersurface M 0 .