DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, April 21 Communications 326 3:45 pm

The free-boundary in the Gauss curvature flow with flat sides

Panagiota Daskalopoulos (University of California, Irvine)

We will discuss the motion of a compact weakly convex two-dimensional surface Σ with flat sides under the Gauss Curvature Flow. We will show that under certain conditions on the initial surface Σ(0), the Gauss Curvature Flow admits a solution Σ(t), in 0 < t ≤ T, for some time T > 0, and the junction curve Γ(t) between the flat and the strictly convex side is a smooth free-boundary, propagating with finite speed.