1305.5470 (Laura Gioia Andrea Keller et al.)

Embedded surfaces of arbitrary genus minimizing the Willmore energy
under isoperimetric constraint    [PDF]

Laura Gioia Andrea Keller, Andrea Mondino, Tristan Rivière

The isoperimetric ratio of an embedded surface in $R^3$ is defined as the ratio of the area of the surface to power three to the squared enclosed volume. The aim of the present work is to study the minimization of the Willmore energy under fixed isoperimetric ratio when the underlying abstract surface has fixed genus $g\geq 0$. The corresponding problem in the case of spherical surfaces, i.e. $g=0$, was recently solved by Schygulla with different methods.

View original: http://arxiv.org/abs/1305.5470