Abstract or Additional Information
The isoperimetric problem (fencing the largest possible area with a fence of given length) is one of the oldest problems in mathematics. In many classical settings it is well understood, whereas in complicated geometries it still gives rise to unsolved problems.
On the other hand, in the recent decades a fruitful analytical tool has emerged, namely deformation of complicated geometric objects to simpler ones using curvature flows. This method has culminated in the proof of the Poincaré conjecture by Hamilton and Perelman.
In this talk we have a look at this technique and use it to solve isoperimetric and related problems. The methods are on the edge between partial differential equations and differential geometry.