Ancient mean curvature flows from minimal hypersurfaces

Abstract

For $n\ge 2$, we construct $I$-dimensional family of embedded ancient solutions to mean curvature flow arise from an unstable minimal hypersurface $\hat{I}\pounds$ with finite total curvature in ${\mathbb{R}}^{n+1}$, where $I$ is the Morse index of the Jacobi operator on $\hat{I}\pounds$.

Final version, to appear in a journal