Deforming submanifolds of arbitrary codimension in a sphere

Abstract

In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere ${\mathbb{S}}^{n+d}$ under integral curvature conditions. As a consequence, we obtain several differentiable sphere theorems for certain submanifolds in ${\mathbb{S}}^{n+d}$.

20 pages

References in corpus (1)

• Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces