Thur, Feb 20 @ 4pm, McH 4130

Isoperimetric problems and geometric flows

The classic isoperimetric problem is a problem of finding optimal relationship between area and perimeter– one can trace it back to Queen Dido. There are similar isoperimetric problems related to other geometric quantities, like total mean curvature, surface area, volume, etc. For these calculus of variations problems, geometric flow is an effective path to the optimal solution. Flows can be specially designed to fit to the underlying geometric structures. They can take the form of generalized mean curvature or inverse mean curvature type flows. We will discuss some recent results in this direction, and main ideas associated to the approach.