  We derive a macroscopic limit for a sharp interface version of a model
proposed in [29] to investigate pattern formation due to competition of
chemical and mechanical forces in biomembranes. We identify sub- and
supercrital parameter regimes and show with the introduction of the
autocorrelation function that the ground state energy leads to the
isoperimetric problem in the subcritical regime, which is interpreted to not
form fine scale patterns.
