  We present the essential findings of the screening theory of the integer
quantum Hall effect (IQHE) considering a quantum point contact (QPC). Our
approach is to solve the Poisson and the Schroedinger equations
self-consistently, taking into account electron interactions, within a Hartree
type approximation for a two dimensional electron gas (2DEG) subject to high
perpendicular magnetic fields. The Coulomb interaction between the electrons
separates 2DEG into two co-existing regions, namely quasi-metallic compressible
and quasi-insulating incompressible regions, which exhibit peculiar screening
and transport properties. In the presence of an external current, we show that
this current is confined into the incompressible regions where the drift
velocity is finite. In particular, we investigate the distribution of these
incompressible strips and their relation with the quantum Hall plateaus
considering a quasi 1D constriction, i.e. a QPC.
