The concept of frustrated phase separation is applied to investigate its co
nsequences for the electronic structure of the high T-c cuprates. The resul
ting incommensurate charge density wave (CDW) scattering is most effective
in creating local gaps in k-space when the scattering vector connects state
s with equal energy. Starting from an open Fermi surface we find that the r
esulting CDW is oriented along the (10)- and (or) (01)-direction which allo
ws for a purely one-dimensional or a two-dimensional "eggbox type" charge m
odulation. In both cases the van Hove singularities are substantially enhan
ced, and the spectral weight of Fermi surface states near the M-points, ten
ds to be suppressed. Remarkably, a leading edge gap arises near these point
s, which, in the eggbox case, leaves finite arcs of the Fermi surface gaple
ss. We discuss our results with repect to possible consequences for photoem
ission experiments.