Prof. Dr. Ben Lambert:
The inverse mean curvature flow perpendicular to the sphere
Time and place
Tuesday, 21.7.15, 16:15-17:15, Raum 404, Eckerstr. 1
Abstract
Usually the inverse mean curvature flow (IMCF) of convex hypersurfaces exists for all time and flows outwards towards infinitely large spheres. In this talk we will consider IMCF on of convex disks inside the unit ball with a Neumann boundary condition on the sphere. We will see that conversely to the boundaryless case, global singularities occur in finite time, and the flow converges in C^{1,\bbeta} to a flat disk. Furthermore we will see that this result is sharp in the sense that if we perturb the boundary manifold, the result does not hold.