  The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect
(QHE) regime are divided into alternating metallic and insulating strips, with
their widths determined by the energy gaps of the QHE states and the
electrostatic Coulomb interaction. Local probing of these submicrometer
features, however, is challenging due to the buried 2DEG structures. Using a
newly developed microwave impedance microscope, we demonstrate the real-space
conductivity mapping of the edge and bulk states. The sizes, positions, and
field dependence of the edge strips around the sample perimeter agree
quantitatively with the self-consistent electrostatic picture. The evolution of
microwave images as a function of magnetic fields provides rich microscopic
information around the \nu = 2 QHE state.
