# Minimization of the Willmore functional under isoperimetric constraint

## Laura Keller

### (EPFL Lausanne Switzerland)

Date: Jul 03, 2014, time: 16:20

Abstract. The Willmore energy of an immersion of an abstract oriented surface is given by the squared mean curvature integrated with respect to the induced volume form.
We study the minimization of this energy under the constraint of given isoperimetric ratio, i.e. under prescribed area and prescribed enclosed volume and for underlying abstract surfaces of positive genus. For this problem we present existence and regularity results.