A new lower bound of the Hausdorff measure of the Sierpinski gasket

Abstract

For the Sierpinski gasket, by using a sort of cover consisting of special regular hexagons, we define a new measure that is equivalent to the Hausdorff measure and obtain a lower bound of this measure. Moreover, the following lower bound of the Hausdroff measure of the Sierpinski gasket has been achieved $$H^s (S) \geqslant 0.670432,$$ where S denotes the Sierpinski gasket, s =dimH(S) =log 23, and Hs(S) denotes the s-dimensional Hausdorff measure of S. The above result improves that developed in ba][2].