Lens bound on a reconstructed Fermi pocket ($A_{\max }=2k_F^2\arccos (K/k_F)-2K\sqrt{k_F^2-K^2}$)

In rectangular-lattice Fermi-surface reconstruction, the zero-coupling closed orbit is the overlap lens of two equal circles of radius $k_F$ with centres separated by $2K$. Two circular sectors minus their triangular portions giveAt fixed chemical potential, the upper hybridized energy band rises when the magnitude of the Fourier coefficient increases. Its occupied pocket therefore shrinks, so this lens is an upper bound in the two-wave model. It is not a universal bound for arbitrary changes of chemical potential or additional energy bands.