Exceptional hyperbolic 3-manifolds

Abstract

We correct and complete a conjecture of D. Gabai, R. Meyerhoff and N. Thurston on the classification and properties of thin tubed closed hyperbolic 3-manifolds. We additionally show that if $N$ is a closed hyperbolic 3-manifold, then either $N=Vol3$ or $N$ contains a closed geodesic that is the core of an embedded tube of radius $\log (3)/2$.