  We consider the Loewner differential equation generating univalent maps of
the unit disk (or of the upper half-plane) onto itself minus a single slit. We
prove that the circular slits, tangent to the real axis are generated by
H\"older continuous driving terms with exponent 1/3 in the Loewner equation.
Singular solutions are described, and the critical value of the norm of driving
terms generating quasisymmetric slits in the disk is obtained.

Complex Variables