  Uniform Harnack inequalities for harmonic functions on the pre- and graphical
Sierpinski carpets are proved using a probabilistic coupling argument. Various
results follow from this, including the construction of Brownian motion on
Sierpinski carpets embedded in $\R^d$, $d\geq 3$, estimates on the fundamental
solution of the heat equation, and Sobolev and Poincar\'e inequalities.
