  We use dynamic scanning capacitance microscopy (DSCM) to image compressible
and incompressible strips at the edge of a Hall bar in a two-dimensional
electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives
access to the complex local conductance, Gts, between a sharp metallic tip
scanned across the sample surface and ground, comprising the complex sample
conductance. Near integer filling factors we observe a bright stripe along the
sample edge in the imaginary part of Gts. The simultaneously recorded real part
exhibits a sharp peak at the boundary between the sample interior and the
stripe observed in the imaginary part. The features are periodic in the inverse
magnetic field and consistent with compressible and incompressible strips
forming at the sample edge. For currents larger than the critical current of
the QHE break-down the stripes vanish sharply and a homogeneous signal is
recovered, similar to zero magnetic field. Our experiments directly illustrate
the formation and a variety of properties of the conceptually important QHE
edge states at the physical edge of a 2DEG.
