Speaker
Description
The area preserving curve shortening flow with Neumann free boundary conditions shortens a curve that is attached perpendicularly to a bounded domain $\Omega$ in the plane but keeps the enclosed area fixed. The end points of that curve move in the boundary curve of $\Omega$. Its limits are candidates for minimizers for the relative isoperimetric problem in the plane (thus, they are circular arcs). We describe the analytical nature of that flow and how the geometry helps to obtain results. Difficulties arise from the non-local nature of the flow. One recent result includes quantitative stability of critical points of the corresponding variational problem which is obtained with the help of the flow. Part of this talk is based on work obtained together with R. Neumayer, J. Park and M. Rupflin.