题目：Curvature Flow of Pinched Hypersurfaces in Space Forms
时间: 2020年5月19日 10:00-11:00
摘要: In this talk, I first introduce mean curvature flow briefly, and then mainly consider closed hypersurfaces immersed in a space of constant sectional curvature evolving in direction of its outer unit normal vector with speed given by a general curvature function of principal curvatures, such that the initial hypersurface is pinched in the sense that the ratio of the biggest and smallest principal curvatures of the hypersurface is close enough to 1 everywhere. We prove that the pinching is preserved as long as the flow exists, and the flow shrinks to a point in finite time. Especially, if the speed is a high order homogeneous function, the normalized flow exists for all time and converges smoothly and exponentially to a round sphere in Euclidean space.
ID：985 353 595
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