  Using the proof of Willmore's conjecture by Marques and Neves, we conjecture
that the free energy of tensionless fluid membranes of arbitrary genus has an
upper bound. This implies that the average genus of such a membrane, in
equilibrium, is finite, regardless of external constraints. We propose that the
Gaussian rigidity may be determined by measuring the relative frequencies of
large-genus configurations at low temperature.

Soft Condensed Matter;Statistical Mechanics