Minimization of bending energies under constraints
Matthias Roeger, TU Dortmund
Biomembranes form the outer boundary of cells and define separated structures inside the cell.
The reduction of a suitable bending energy, whose prototype is the classical Willmore functional
for surfaces, contributes to the shape of such membranes. In the case of inner structures this
motivates the following variational problem: minimize the Willmore energy in the class of
smooth embeddings of the sphere that have prescribed surface area a>0 and are confined
to the unit ball. We investigate the dependence of the minimal energy value on the parameter a.
(Joint work with Stefan Mueller, Bonn.)