Lower functions for the support of super-Brownian motion

The aim of this paper is to describe the minimum speed at which a super-Brownian motion starting at the Dirac mass at 0 moves away from its initial point. More precisely, we consider the class of functions and then determine the values of [kappa] such that the support of super-Brownian motion exits the ball of radius [phi][kappa](t) before time t, for every t small enough.