  Fermi surface models applied to the underdoped cuprates predict the small
pocket area to be strongly dependent on doping whereas quantum oscillations in
YBa2Cu3O6+x find precisely the opposite to be true; seemingly at odds with the
Luttinger volume. We show that such behavior can be explained by an
incommensurate antinodal Fermi surface nesting-type instability; further
explaining the doping-dependent superstructures seen in cuprates using scanning
tunneling microscopy. We develop a Fermi surface reconstruction scheme
involving orthogonal density waves in two-dimensions and show that their
incommensurate behavior requires momentum-dependent coupling. A co-operative
modulation of the charge and bond-strength is therefore suggested.
