Ancient Gauss Curvature Flows of Bounded Width

Abstract

In this paper, we construct a pancake-like ancient compact solution with flat sides to the Gauss curvature flow, contained in a slab. Also, we construct sausage-like ancient compact solutions to the $\hat{I}\pm$-Gauss curvature flow with $\hat{I}\pm >\frac{1}{2}$, asymptotic to a round cylinder.

26 pages, 4 figures