  We extend the results on the uniform convergence of Bieberbach polynomials to
domains with certain interior zero angles (outward pointing cusps), and show
that they play a special role in the problem. Namely, we construct a
Keldysh-type example on the divergence of Bieberbach polynomials at an outward
pointing cusp and discuss the critical order of tangency at this interior zero
angle, separating the convergent behavior of Bieberbach polynomials from the
divergent one for sufficiently thin cusps.
