On the Distortion Theorem for Quasiconformal Mappings with Fixed Boundary Values1

For a planar domain with at least three boundary points and the hyperbolic metric of with constant curvature 1, G. J. Martin poses a problem that asks, if f is a K-quasiconformal self-homeomorphism of with boundary values given by the identity mapping, whether Ž z, f Ž z.. log K holds for z, f Ž z. . In this note, we give a negative answer to this question.