Upper Bounds of the Hausdorff Measure of the Sierpinski Gasket
by
Li Feng
Darton College, 2400 Gillionville Road, Albany, GA 31707
Coauthors: Zuoling Zhou

We show that the Hausdorff measure of a set with positive Hausdorff dimension is a a sequential limit. For self-similar sets satisfying the open set condition, we develop a general method to calculate the upper bounds of the Hausdorff measure. As an application, we show that the Hausdorff measure of the Sierpinski gasket is upper bounded by a one variable continuous function. We develop the hexagon method and the dodecagon method to achieve better upper bounds of the Hausdorff measure of the Sierpinski gasket.

Date received: February 17, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-45.