Every smooth convex surface collapses to a point under the mean-curvature flow, without other singularities, and converges to the shape of a sphere as it does so. For surfaces of dimension two or more this is a theorem of Gerhard Huisken; for the one-dimensional curve-shortening flow it is the Gage–Hamilton–Grayson theorem. However, there exist embedded surfaces of two or more dimensions other than the sphere that stay self-similar as they contract to a point under the mean-curvature flow, including the Angenent torus.