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.