A bound on the free energy of tensionless membranes

TL;DR

This paper conjectures an upper bound on the free energy of tensionless fluid membranes of any genus, implying a finite average genus in equilibrium, and suggests measuring Gaussian rigidity via low-temperature configurations.

Contribution

It introduces a conjecture linking free energy bounds to membrane genus and proposes a method to determine Gaussian rigidity through configuration frequency analysis.

Findings

Conjecture of an upper bound on free energy for tensionless membranes.

Finite average genus in equilibrium regardless of external constraints.

Proposed measurement method for Gaussian rigidity using low-temperature configurations.

Abstract

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.