  A fundamental step in the analysis of singularities of Ricci flow was the
discovery by Perelman of a monotonic volume quantity which detected shrinking
solitons in (arXiv:math/0211159). A similar quantity was found by Feldman,
Ilmanen, and Ni in 2005 which detected expanding solitons. The current work
introduces a modified length functional as a first step towards a steady
soliton monotonicity formula. This length functional generates a distance
function in the usual way which is shown to satisfy several differential
inequalities which saturate precisely on manifolds satisfying a modification of
the steady soliton equation.
