Deforming submanifolds of arbitrary codimension in a sphere

Details Deforming submanifolds of arbitrary codimension in a sphere Deforming submanifolds of arbitrary codimension in a sphere

2012-03-31

arxiv.org/abs/1204.0106v1

Mathematics

Differential Geometry

20 pages

Scientific paper

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 $\mathbb{S}^{n+d}$.

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