The dimension of the boundary of super-Brownian motion

We show that the Hausdorff dimension of the boundary of d-dimensional super-Brownian motion is $$0$$, if $$d=1$$; $$4-2\sqrt{2}$$, if $$d=2$$; and $$(9-\sqrt{17})/2$$, if $$d=3$$. This is a joint work with Leonid Mytnik.