Title: A Liouville Theorem for Mean Curvature Flow,
Abstract: Ancient solutions arise in the study of parabolic blow-ups. If we can
categorize ancient solutions, we can better understand blow-up limits. Based on
an argument of Giga and Kohn, we give a Liouville-type theorem restricting
ancient, type-I, non-collapsing two- dimensional mean curvature flows to either
spheres or cylinders.