Copyright © 2010 Peter Hästö et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We show that the equivalence of the Apollonian metric
and its inner metric remains unchanged by the removal of a point from the
domain. For this we need to assume that the complement of the domain is not
contained in a hyperplane. This improves a result of the authors wherein the
same conclusion was reached under the stronger assumption that the domain
contains an exterior point.