  In the asymptotic limit $Q^2 \gg m^2$, the heavy quark form factors exhibit
Sudakov behavior. We study the corresponding renormalization group equations of
the heavy quark form factors which do not only govern the structure of infrared
divergences, but also control the high energy logarithms. This enables us to
obtain the complete logarithmic three--loop and partial four--loop
contributions to the heavy quark form factors in perturbative Quantum
Chromodynamics.
