In order to explain the bi-concave shape of red blood cells, Helfrich proposed to study the minimisation of a bending energy amongst closed surfaces with given fixed area and volume. In the homogeneous case, the Helfrich functional simplifies to the scaling invariant Willmore functional. Thus, for the minimisation, the two constraints on area and volume reduce to a single constraint on the scaling invariant isoperimetric ratio. This talk is about two strict inequalities that lead to the existence of isoperimetric constrained Willmore tori.

Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact the host to get the link.

Host: Peter McGrath, pjmcgrat@ncsu.edu