  We study the density X(t,x) of one-dimensional super-Brownian motion and find
the asymptotic behaviour of P(0<X(t,x)<a) as a approaches 0, as well as the
Hausdorff dimension of the boundary of the support of X(t). The answers are in
terms of the lead eigenvalue of the Ornstein-Uhlenbeck generator with a
particular killing term. This work is motivated in part by questions of
pathwise uniqueness for associated stochastic partial differential equations.
