Pure and Applied Mathematics Quarterly
Volume 11 (2015)
Contracting pinched hypersurfaces in spheres by their mean curvature
Pages: 329 – 368
In this paper, we study an open problem proposed in . We prove that the mean curvature flow of hypersurfaces in the sphere will contract to a round point in finite time if the initial hypersurface satisfies a curvature pinching condition. Our theorem is a partial improvement of the convergence theorem due to Huisken .
mean curvature flow, hypersurface, sphere, curvature pinching
2010 Mathematics Subject Classification