## PDE and Differential Geometry Seminar

# Ancient Pancakes

## Theodora Bourni (University of Tennessee Knoxville )

### Monday, March 5, 2018
2:30 pm

MONT 214

We construct a compact, convex ancient solution of mean curvature flow in $\\R^{n 1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $\pi$ and in no smaller slab. This work is joint with Mat Langford and Giuseppe Tinaglia.