  In this paper we introduce the channel of energy argument to the study of
energy critical wave maps into the sphere. More precisely, we prove a channel
of energy type inequality for small energy wave maps, and as an application we
show that for a wave map that has energy just above the degree one harmonic
maps and that blows up in finite time, the solution asymptotically de-couples
into a regular part plus a traveling wave with small momentum, in the energy
space. In particular, the only possible form of energy concentration is through
the concentration of traveling waves. This is often called quantization of
energy at blow up. We also give a brief review of important background results
in the subcritical and critical regularity theory for the two dimensional wave
maps.
