We give the first explicit lower bound for the length of a geodesic in a closed orientable hyperbolic 3-manifold M of lowest volume. We also give an upper bound for the tube radius of any shortest geodesic in M. We explain how these results might be the first steps towards a rigorous computer assisted effort to determine the least volume closed orientable hyperbolic 3-manifold(s).
"Volumes of Tubes in Hyperbolic 3-Manifolds." J. Differential Geom. 57 (1) 23 - 46, January, 2001. https://doi.org/10.4310/jdg/1090348088