Gradient bounds on the free boundary for the mean curvature flow of graphs
Abstract: In this talk we present a way to obtain gradient bounds on the free boundary for graphs evolving by mean curvature flow with a ninety degree angle condition on a fixed surface in 3-dimensional Euclidean space. The contact surface is required to be rotationally symmetric. There are two types of bad gradient behaviour on the free boundary. We will focus on the one we call a tilt, which is when the evolving surfaces lose the graph property by the normal of the graphs turning in the direction of the rotation vector field of the contact surface. We present a complete list of curvature properties for the evolving graphs at a first point of tilt and give sufficient conditions on the contact surface for which this behaviour is excluded.

Brakkes mean curvature flow, part I
Please note: starting time 4.15 pm