ABSTRACT: It is shown by using asymptotic Hamilton sequences that there is always a substantial point p on the boundary of a plane domain of arbitrary connectivity. That is, H_p=H, where H is the boundary dilatation and H_p is the local dilatation at p. It is also shown that the sets of infinitesimally substantial and substantial points coincide.
The paper is a part of IN THE TRADITION OF AHLFORS AND BERS , Contemporary Mathematics, Vol. 256, AMS.
This volume is based on the Proceedings of the first Ahlfors-Bers Colloquium, held in Stony Brook in November 1998.