## Isoperimetric Problems Between Analysis and Geometry

# Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint

## Andrea Mondino (University of Warwick)

19 jun 2014 -- 14:00 [open in google calendar]

**Abstract.**

The isoperimetric ratio of an embedded surface in R3 is defined as the ratio of the area of the surface to power three to the squared enclosed volume. The Willmore energy is defined as the L2 norm of the mean curvature of the surface. Motivated by the Helfrich model in cell biology, we study the minimization of the Willmore energy under fixed isoperimetric ratio when the underlying abstract surface has fixed genus g ≥ 0. This is joint work with Tristan Rivire (ETH) and Laura Keller (EPFL).