Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type

Abstract

For each $n\ge 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in ${\mathbb{R}}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\times S^{n-1}\times S^1$ and are $SO(n)\times SO(n)$ invariant. The method is inspired by constructions of Hsiang and these surfaces generalize self-shrinking "tori" diffeomorphic to $S^{n-1}\times S^1$ constructed by Angenent.