Before revision:  If d \geq 4, the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in  R^d that we call the minimum curvature flow.
After revision:  If d \geq 4, the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in \mathbb R^d that we call the minimum curvature flow.